{"id":16772,"date":"2022-04-06T09:43:28","date_gmt":"2022-04-06T04:13:28","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=16772"},"modified":"2022-04-07T11:14:11","modified_gmt":"2022-04-07T05:44:11","slug":"big-ideas-math-answers-grade-6-chapter-10","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-6-chapter-10\/","title":{"rendered":"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays"},"content":{"rendered":"<p><strong>Big Ideas Math Answers Grade 6 Chapter 10 Data Displays:<\/strong> Free Download Big Ideas Math Answers Grade 6 Chapter 10 Data Displays Pdf here. Get step by step solution to all the concepts of Stem-and-Leaf Plots, Histograms, Shapes of Distributions, Choosing Appropriate Measures, and so on. Download Answer Key of Big Ideas Math 6th Grade Chapter 10 Data Displays Pdf for free of cost.<\/p>\n<p>Start your preparation with the given material and know-how to manage your time and your strengths and weaknesses. <a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-6\/\">Big Ideas Math Answers Grade 6 <\/a>Data Displays problems will help you to score more marks in the exam. Follow the below sections to get the detailed material and concepts of data displays.<\/p>\n<h2>Big Ideas Math Book 6th Grade Answer Key Chapter 10 Data Displays<\/h2>\n<p>Do you wanna master in data displays concept? It requires a lot of preparation and dedication to get perfect in this concept. To master this concept, you have to check BIM Math 6th Grade Answer Key Chapter 10 Data Displays pdf. With the help of this article, you can easily prepare the timetable.<\/p>\n<p>If you prepare the timetable, you can easily know the time available to cover each chapter of the concept. There are several chapters involved in this concept. Make use of the Big Ideas Math Grade 6 Solution Key which acts as a teacher for you in your complete preparation. Follow the <strong>Big Ideas Math Book 6th Grade Answer Key Chapter 10 Data Displays<\/strong> and overcome your weaknesses.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<ul>\n<li><a href=\"#Data_Displays_STEAM_Video_\/_Performance_Task\">Data Displays STEAM Video\/Performance Task<\/a><\/li>\n<li><a href=\"#Data_Displays_Getting_Ready_for_Chapter_10\">Data Displays Getting Ready for Chapter 10<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 1 &#8211; Stem-and-Leaf Plots<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.1_Stem_and_Leaf_Plots\">Lesson 10.1 Stem-and-Leaf Plots<\/a><\/li>\n<li><a href=\"#Stem_and_Leaf_Plots_Homework_&amp;_Practice_10.1\">Stem-and-Leaf Plots Homework &amp; Practice 10.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 2 &#8211; Histograms<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.2_Histograms\">Lesson 10.2 Histograms<\/a><\/li>\n<li><a href=\"#Histograms_Homework_&amp;_Practice_10.2\">Histograms Homework &amp; Practice 10.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 3 &#8211; Shapes of Distributions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.3_Shapes_of_Distributions\">Lesson 10.3 Shapes of Distributions<\/a><\/li>\n<li><a href=\"#Shapes_of_Distributions_Homework_&amp;_Practice_10.3\">Shapes of Distributions Homework &amp; Practice 10.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 4 &#8211; Choosing Appropriate Measures<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.4_Choosing_Appropriate_Measures\">Lesson 10.4 Choosing Appropriate Measures<\/a><\/li>\n<li><a href=\"#Choosing_Appropriate_Measures_Homework_&amp;_practice_10.4\">Choosing Appropriate Measures Homework &amp; Practice 10.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 5 &#8211; Box-and-Whisker Plots<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.5_Box_and_Whisker_Plots\">Lesson 10.5 Box-and-Whisker Plots<\/a><\/li>\n<li><a href=\"#Box_and_Whisker_Plots_Homework_&amp;_Practice_10.5\">Box-and-Whisker Plots Homework &amp; Practice 10.5<\/a><\/li>\n<\/ul>\n<p><strong>Data Displays<\/strong><\/p>\n<ul>\n<li><a href=\"#Data_Displays_Connecting_Concepts\">Data Displays Connecting Concepts<\/a><\/li>\n<li><a href=\"#Data_Displays_Chapter_Review\">Data Displays Chapter Review<\/a><\/li>\n<li><a href=\"#Data_Displays_Practice_Test\">Data Displays Practice Test<\/a><\/li>\n<li><a href=\"#Data_Displays_Cumulative_Practice\">Data Displays Cumulative Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Data_Displays_STEAM_Video_\/_Performance_Task\"><\/a>Data Displays STEAM Video\/Performance Task<\/h3>\n<p><strong>STEAM Video<\/strong><br \/>\nChoosing a Dog<br \/>\nDifferent animals grow at different rates. Given a group of puppies, describe an experiment that you can perform to compare their growth rates. Describe a real-life situation where knowing an animal\u2019s growth rate can be useful.<\/p>\n<p>Watch the STEAM Video \u201cChoosing a Dog.\u201d Then answer the following questions.<br \/>\n1. Using Alex and Tony\u2019s stem-and-leaf plots below, describe the weights of most dogs at 3 months of age and 6 months of age.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16773\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 1\" width=\"617\" height=\"265\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-1.png 617w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-1-300x129.png 300w\" sizes=\"(max-width: 617px) 100vw, 617px\" \/><\/p>\n<p>Answer:<br \/>\nWeight of dogs at 3 months:<br \/>\n29, 34, 40, 40, 41, 42, 44, 46, 47, 48, 48, 53<br \/>\nWeight of dogs at 6 months:<br \/>\n57, 58, 61, 61, 63, 64, 65, 65, 65, 66, 67, 73<br \/>\n2. Make predictions about how the stem-and-leaf plot will look after 9 months and after 1 year.<br \/>\nWeight of dogs at 9 months<br \/>\n77, 78, 81, 81, 83, 84, 85, 85, 85, 86, 87, 91<br \/>\nWeight of dogs at 1 year<br \/>\n87, 88, 89, 93, 94, 95, 95, 95, 95, 96, 97, 99<\/p>\n<p><strong>Performance Task<\/strong><br \/>\nClassifying Dog Breeds by Size<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16774\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-2.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 2\" width=\"263\" height=\"328\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-2.png 263w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-2-241x300.png 241w\" sizes=\"(max-width: 263px) 100vw, 263px\" \/><br \/>\nAfter completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task. You will be given names, breeds, and weights of full-grown dogs at a shelter.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16775\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-3.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 3\" width=\"320\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-3.png 320w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-3-300x99.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><br \/>\nYou will use a data display to make conclusions about the sizes of dogs at the shelter. Why might someone be interested in knowing the sizes of dogs at a shelter?<\/p>\n<p>Answer:<br \/>\nBecause they need time to adjust.<br \/>\nYou can buy the dog shelter based on the height and weight of the dogs.<\/p>\n<h3><a id=\"Data_Displays_Getting_Ready_for_Chapter_10\"><\/a>Data Displays Getting Ready for Chapter 10<\/h3>\n<p><strong>Chapter Exploration<\/strong><br \/>\nWork with a partner. A famous data set was collected in Scotland in the mid-1800s. It contains the chest sizes(in inches) of 5738 men in the Scottish Militia.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16776\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-4.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 4\" width=\"518\" height=\"341\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-4.png 518w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-4-300x197.png 300w\" sizes=\"(max-width: 518px) 100vw, 518px\" \/><br \/>\n1. Describe the shape of the bar graph shown above.<\/p>\n<p>Answer: The shape of the above graph is Histogram.<\/p>\n<p>2. Which of the following data sets have a bar graph that is similar in shape to the bar graph shown above? Assume the sample is selected randomly from the population. Explain your reasoning.<br \/>\na. the heights of 500 women<br \/>\nb. the ages of 500 dogs<br \/>\nc. the last digit of 500 phone numbers<br \/>\nd. the weights of 500 newborn babies<\/p>\n<p>Answer: The last digit of 500 phone numbers is similar in shape to the bar graph shown above.<\/p>\n<p>3. Describe two other real-life data sets, one that is similar in shape to the bar graph shown above and one that is not.<\/p>\n<p>Answer: The height of 500 students in the school and age of students in the classroom.<\/p>\n<p><strong>Vocabulary<\/strong><br \/>\nThe following vocabulary terms are defined in this chapter. Think about what each term might mean and record your thoughts.<br \/>\nstem-and-leaf plot<br \/>\nbox-and-whisker plot<br \/>\nfrequency table<br \/>\nfive-number summary<\/p>\n<p>Answer:<br \/>\ni. stem-and-leaf plot: A stem-and-leaf display or stem-and-leaf plot is a device for presenting quantitative data in a graphical format, similar to a histogram, to assist in visualizing the shape of a distribution.<br \/>\nii. A box and whisker plot\u2014also called a box plot\u2014displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median.<br \/>\niii. In statistics, a frequency distribution is a list, table, or graph that displays the frequency of various outcomes in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval.<br \/>\niv. The five-number summary is a set of descriptive statistics that provides information about a dataset.<\/p>\n<h3><a id=\"Lesson_10.1_Stem_and_Leaf_Plots\"><\/a>Lesson 10.1 Stem-and-Leaf Plots<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Making a Data Display<br \/>\nWorkwith a partner. The list below gives the ages of women when they became first ladies of the United States.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16777\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 1\" width=\"608\" height=\"536\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-1.png 608w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-1-300x264.png 300w\" sizes=\"(max-width: 608px) 100vw, 608px\" \/><br \/>\na. The incomplete data display shows the ages of the first ladies in the left column of the list above. What do the numbers on the left represent? What do the numbers on the right represent?<br \/>\nb. This data display is called a stem-and-leaf plot. What numbers do you think represent the stems? leaves? Explain your reasoning.<br \/>\nc. Complete the stem-and-leaf plot using the remaining ages.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-28420\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-1-300x264.jpg\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-1\" width=\"300\" height=\"264\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-1-300x264.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-1.jpg 608w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe tens place represents the stem and the ones place represents the leaf.<br \/>\nd. <strong>REASONING<\/strong><br \/>\nWrite a question about the ages of first ladies that is easier to answer using a stem-and-leaf plot than a dot plot.<br \/>\nAnswer: Make the stem and leaf plot to find the ages of the first ladies.<br \/>\nBy using the above data you can make the stem and leaf plot easily.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-16778\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-2.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 2\" width=\"193\" height=\"257\" \/><\/p>\n<p><strong>Key Idea<\/strong><br \/>\nStem-and-Leaf Plots<br \/>\nA stem-and-leaf plot uses the digits of data values to organize a data set. Each data value is broken into a stem(digit or digits on the left) and a leaf(digit or digits on the right).<br \/>\nA stem-and-leaf plot shows how data are distributed.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16779\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-4.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 4\" width=\"307\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-4.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-4-300x173.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><\/p>\n<p><strong>EXAMPLE 1<\/strong><\/p>\n<p>Making a Stem-and-Leaf Plot<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16780\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-5.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 5\" width=\"167\" height=\"223\" \/><br \/>\nMake a stem-and-leaf plot of the lengths of the 12 phone calls.<br \/>\nStep 1: Order the data.<br \/>\n2, 3, 5, 6, 10, 14, 18, 23, 23, 30, 36, 55<br \/>\nStep 2: Choose the stems and the leaves. Because the data values range from 2 to 55, use the tens digits for the stems and the ones digits for the leaves. Be sure to include the key.<br \/>\nStep 3: Write the stems to the left of the vertical line.<br \/>\nStep 4: Write the leaves for each stem to the right of the vertical line.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16781\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-6.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 6\" width=\"454\" height=\"192\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-6.png 454w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-6-300x127.png 300w\" sizes=\"(max-width: 454px) 100vw, 454px\" \/><\/p>\n<p><strong>Try It<\/strong><br \/>\nQuestion 1.<br \/>\nMake a stem-and-leaf plot of the hair lengths.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16782\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-7.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 7\" width=\"444\" height=\"97\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-7.png 444w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-7-300x66.png 300w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><br \/>\nAnswer:<br \/>\nStep 1: Order the data.<br \/>\n1, 1, 1, 2, 2, 4, 5, 5, 7, 12, 20, 23, 27, 30, 32, 33, 38, 40, 44, 47<br \/>\nStep 2: Choose the stems and the leaves. Because the data values range from 1 to 47, use the tens digits for the stems and the ones digits for the leaves. Be sure to include the key.<br \/>\nStep 3: Write the stems to the left of the vertical line.<br \/>\nStep 4: Write the leaves for each stem to the right of the vertical line.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-28423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-12-Data-Displays-img_5-300x200.jpg\" alt=\"Big Ideas Math Answers Grade 6 Chapter 12 Data Displays img_5\" width=\"300\" height=\"200\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-12-Data-Displays-img_5-300x200.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-12-Data-Displays-img_5.jpg 354w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>EXAMPLE 2<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16783\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-8.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 8\" width=\"207\" height=\"168\" \/><br \/>\nThe stem-and-leaf plot shows student quiz scores. (a) How many students scored less than 8 points? (b) How many students scored at least 9 points? (c) How are the data distributed?<br \/>\na. There are \ufb01ve scores less than 8 points:<br \/>\n6.6, 7.0, 7.5, 7.7, and 7.8.<br \/>\nFive students scored less than 8 points.10<br \/>\nb. There are four scores of at least 9 points:<br \/>\n9.0, 9.2, 9.9, and 10.0.<br \/>\nFour students scored at least 9 points.<br \/>\nc. There are few low quiz scores and few high quiz scores. So, most of the scores are in the middle, from 8.1 to 8.9 points.<\/p>\n<p><strong>Try It<\/strong><br \/>\nQuestion 2.<br \/>\nUse the grading scale at the right.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16784\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-9.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 9\" width=\"137\" height=\"108\" \/><br \/>\na. How many students received a B on the quiz?<br \/>\nAnswer: There are 9 students who received a B on the quiz.<br \/>\nb. How many students received a C on the quiz?<br \/>\nAnswer: There are 4 students who received a C on the quiz.<\/p>\n<p><strong>Self &#8211; Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<br \/>\nQuestion 3.<br \/>\n<strong>MAKING A STEM-AND-LEAF PLOT<\/strong><br \/>\nMake a stem-and-leaf plot of the data values 14, 22, 9, 13, 30, 8, 25, and 29.<br \/>\nAnswer:<br \/>\nThe ones represent the leaf and the tens place represent the stem.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29048\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_6.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 10 Data Displays img_6\" width=\"236\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_6.jpg 236w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_6-150x150.jpg 150w\" sizes=\"(max-width: 236px) 100vw, 236px\" \/><\/p>\n<p>Question 4.<br \/>\n<strong>WRITING<\/strong><br \/>\nHow does a stem-and-leaf plot show the distribution of a data set?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16785\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-10.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 10\" width=\"164\" height=\"160\" \/><br \/>\nAnswer:<br \/>\n02, 03, 1, 21, 26, 30, 34, 36, 44, 45, 48, 48, 49<\/p>\n<p>Explanation:<br \/>\nA stem-and-leaf display or stem-and-leaf plot is a device for presenting quantitative data in a graphical format, similar to a histogram, to assist in visualizing the shape of a distribution.<\/p>\n<p>Question 5.<br \/>\n<strong>REASONING<\/strong><br \/>\nConsider the stem-and-leaf plot shown.<br \/>\na. How many data values are at most 10?<br \/>\nAnswer: By seeing the above stem and leaf plot we can find the data values of at most 10.<br \/>\nThe data values less than or equal to 10 are 3.<br \/>\nb. How many data values are at least 30?<br \/>\nAnswer: By seeing the above stem and leaf plot we can find the data values of at least 30.<br \/>\nThe data values of less than 30 are 5.<br \/>\nc. How are the data distributed?<br \/>\nAnswer: The data is distributed according to the stem and leaf plot. The tens place is given to the stem and the ones place is given to the leaf.<\/p>\n<p>Question 6.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nHow can you display data whose values range from 82 through 129 in a stem-and-leaf plot?<br \/>\nAnswer:<br \/>\nGiven data range from 82 to 129<br \/>\nConsidering 9 random values between 82 and 129.<br \/>\nFrom the data 86, 91, 93, 100, 107, 109, 113, 122, 124, stem and leaf are calculated for each number.<br \/>\n86 is split into 8 (stem) and 6 (leaf)<br \/>\n91 is split into 9 (stem) and 1 (leaf)<br \/>\n93 is split into 9 (stem) and 3 (leaf)<br \/>\n100 is split into 10 (stem) and 0 (leaf)<br \/>\n107 is split into 10 (stem) and 7 (leaf)<br \/>\n109 is split into 10 (stem) and 9 (leaf)<br \/>\n113 is split into 11 (stem) and 3 (leaf)<br \/>\n122 is split into 12 (stem) and 2 (leaf)<br \/>\n124 is split into 12 (stem) and 4 (leaf)<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-medium wp-image-29055\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_7-164x300.png\" alt=\"Big Ideas Math Grade 6 Chapter 10 Data Displays img_7\" width=\"164\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_7-164x300.png 164w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_7.png 212w\" sizes=\"(max-width: 164px) 100vw, 164px\" \/><\/p>\n<p><strong>EXAMPLE 3<\/strong><br \/>\nModeling Real Life<br \/>\nThe stem-and-leaf plot shows the heights of several houseplants. Use the data to answer the question, \u201cWhat is a typical height of a houseplant?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16786\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-11.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 11\" width=\"219\" height=\"449\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-11.png 219w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-11-146x300.png 146w\" sizes=\"(max-width: 219px) 100vw, 219px\" \/><br \/>\nFind the mean, median, and mode of the data. Use the measure that best represents the data to answer the statistical question.<br \/>\nMean: \\(\\frac{162}{15}\\) = 10.8<br \/>\nMedian: 11<br \/>\nMode: 11<br \/>\nThe mean is slightly less than the median and mode, but all three measures can be used to represent the data.<br \/>\nSo, the typical height of a houseplant is about 11 inches.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16787\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-12.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 12\" width=\"161\" height=\"182\" \/><br \/>\nQuestion 7.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nWork with a partner. Use two number cubes to conduct the following experiment. Then use a stem-and-leaf plot to organize your results and describe the distribution of the data.<br \/>\n\u2022 Toss the cubes and find the product of the resulting numbers. Record your results.<br \/>\n\u2022 Repeat this process 30 times.<br \/>\nAnswer:<br \/>\nFrom the data 15,4,6,30,6,8,36,12,12,6,6,4,15,10,4,2,20,3,15,6,4,6,3,10,3,20,4,12,4,20.<br \/>\nStem and leaf are calculated for each number.<br \/>\n15 is split into 1 (stem) and 5 (leaf)<br \/>\n04 is split into 0 (stem) and 4 (leaf)<br \/>\n06 is split into 0 (stem) and 6 (leaf)<br \/>\n30 is split into 3 (stem) and 0 (leaf)<br \/>\n06 is split into 0 (stem) and 6 (leaf)<br \/>\n08 is split into 0 (stem) and 8 (leaf)<br \/>\n36 is split into 3 (stem) and 6 (leaf)<br \/>\n12 is split into 1 (stem) and 2 (leaf)<br \/>\n12 is split into 1 (stem) and 2 (leaf)<br \/>\n06 is split into 0 (stem) and 6 (leaf)<br \/>\n06 is split into 0 (stem) and 6 (leaf)<br \/>\n04 is split into 0 (stem) and 4 (leaf)<br \/>\n15 is split into 1 (stem) and 5 (leaf)<br \/>\n10 is split into 1 (stem) and 0 (leaf)<br \/>\n04 is split into 0 (stem) and 4 (leaf)<br \/>\n02 is split into 0 (stem) and 2 (leaf)<br \/>\n20 is split into 2 (stem) and 0 (leaf)<br \/>\n03 is split into 0 (stem) and 3 (leaf)<br \/>\n15 is split into 1 (stem) and 5 (leaf)<br \/>\n06 is split into 0 (stem) and 6 (leaf)<br \/>\n04 is split into 0 (stem) and 4 (leaf)<br \/>\n06 is split into 0 (stem) and 6 (leaf)<br \/>\n03 is split into 0 (stem) and 3 (leaf)<br \/>\n20 is split into 2 (stem) and 0 (leaf)<br \/>\n04 is split into 0 (stem) and 4 (leaf)<br \/>\n12 is split into 1 (stem) and 2 (leaf)<br \/>\n04 is split into 0 (stem) and 4 (leaf)<br \/>\n20 is split into 2 (stem) and 0 (leaf)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-29071\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-Math-Grade-6-Chapter-10-Data-Displays-img_8-300x163.png\" alt=\"Big ideas Math Grade 6 Chapter 10 Data Displays img_8\" width=\"300\" height=\"163\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-Math-Grade-6-Chapter-10-Data-Displays-img_8-300x163.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-Math-Grade-6-Chapter-10-Data-Displays-img_8.png 589w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 8.<br \/>\nThe stem-and-leaf plot shows the weights (in pounds) of several puppies at a pet store. Use the data to answer the question, \u201cHow much does a puppy at the pet store weigh?<br \/>\nAnswer:<br \/>\nWe can use the mean of the data. To find the mean, add the data then divide the sum of the number of data<br \/>\n(8+12+15+17+18+24+24+31)\/8 = 149\/8 = 18.625<br \/>\nTo the nearest pound, a puppy weighs about 19 pounds<\/p>\n<h3><a id=\"Stem_and_Leaf_Plots_Homework_&amp;_Practice_10.1\"><\/a>Stem-and-Leaf Plots Homework &amp; Practice 10.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find and interpret the mean absolute deviation of the data.<\/strong><br \/>\nQuestion 1.<br \/>\n8, 6, 8, 5, 3, 10, 11, 5, 7<br \/>\nAnswer:<br \/>\nFirst, arrange the given values in the ascending order.<br \/>\n3, 5, 5, 6, 7, 8, 8, 10, 11<br \/>\nWe find the mean of the data<br \/>\nmean = (3 + 5 + 5 + 6 + 7 + 8 + 8 + 10 + 11)\/9<br \/>\nmean = 7<\/p>\n<p>Question 2.<br \/>\n55, 46, 39, 62, 55, 51, 48, 60, 39, 45<br \/>\nAnswer:<br \/>\nFirst, arrange the given values in the ascending order.<br \/>\n39, 39, 45, 46, 48, 51, 55, 55, 60, 62<br \/>\nWe find the mean of the data<br \/>\nmean = (39 + 39 + 45 + 46 + 48 + 51 + 55 + 55 + 60 + 62)\/10<br \/>\nmean = 50<\/p>\n<p>Question 3.<br \/>\n37, 54, 41, 18, 28, 32<br \/>\nAnswer:<br \/>\nFirst, arrange the given values in the ascending order.<br \/>\n18, 28, 32, 37, 41, 54<br \/>\nWe find the mean of the data<br \/>\nmean = (18+28+32+37+41+54)\/6<br \/>\nmean = 35<\/p>\n<p>Question 4.<br \/>\n12, 25, 8, 22, 6, 1, 10, 4<br \/>\nAnswer:<br \/>\nFirst, arrange the given values in ascending order.<br \/>\n1, 4, 6, 8, 10,12, 22, 25<br \/>\nmean = (1+ 4 + 6 + 8 + 10 + 12 + 22 + 25)\/8<br \/>\nmean = 11<\/p>\n<p><strong>Use the Distributive Property to simplify the expression.<\/strong><br \/>\nQuestion 5.<br \/>\n5(n + 8)<br \/>\nAnswer: 5n + 40<\/p>\n<p>Explanation:<br \/>\n5(n + 8) = 5 \u00d7 n + 5 \u00d7 8<br \/>\n5n + 40<\/p>\n<p>Question 6.<br \/>\n7(y &#8211; 6)<br \/>\nAnswer: 7y &#8211; 42<\/p>\n<p>Explanation:<br \/>\n7(y &#8211; 6) = 7 \u00d7 y &#8211; 7 \u00d7 6<br \/>\n7y &#8211; 42<\/p>\n<p>Question 8.<br \/>\n14(2b + 3)<br \/>\nAnswer: 28b + 42<\/p>\n<p>Explanation:<br \/>\n14(2b + 3) = 14 \u00d7 2b + 14 \u00d7 3<br \/>\n28b + 42<\/p>\n<p>Question 9.<br \/>\n11(9 + s)<br \/>\nAnswer: 99 + 11s<\/p>\n<p>Explanation:<br \/>\n11(9 + s) = 11 \u00d7 9 + 11 \u00d7 s<br \/>\n99 + 11s<\/p>\n<p><strong>Solve the equation.<\/strong><br \/>\nQuestion 9.<br \/>\n\\(\\frac{p}{2}\\) = 8<br \/>\nAnswer: 16<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{p}{2}\\) = 8<br \/>\np = 8 \u00d7 2<br \/>\np = 16<\/p>\n<p>Question 10.<br \/>\n28 = 6g<br \/>\nAnswer: 4.66<\/p>\n<p>Explanation:<br \/>\n28 = 6g<br \/>\ng = 28\/6 = 4.66<br \/>\nThus g = 4.66<\/p>\n<p>Question 11.<br \/>\n3d \u00f7 4 = 9<br \/>\nAnswer: 12<\/p>\n<p>Explanation:<br \/>\n3d \u00f7 4 = 9<br \/>\n3d = 9 \u00d7 4<br \/>\n3d = 36<br \/>\nd = 36\/3<br \/>\nd = 12<br \/>\nThus d = 12<\/p>\n<p>Question 12.<br \/>\n10 = \\(\\frac{2z}{3}\\)<br \/>\nAnswer:<\/p>\n<p>Explanation:<br \/>\n10 = \\(\\frac{2z}{3}\\)<br \/>\n10 \u00d7 3 = 2z<br \/>\n2z = 30<br \/>\nz = 30\/2<br \/>\nz = 15<br \/>\nSo, z = 15<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>REASONING<\/strong><br \/>\nWrite a question that is easier to answer using the stem-and-leaf plot than a dot plot. (See Exploration 1, p. 457.)<br \/>\nQuestion 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16788\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-13.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 13\" width=\"247\" height=\"155\" \/><br \/>\nAnswer:<br \/>\nMake a stem leaf plot to find the number of customers who visit your shop.<br \/>\n12, 13, 16, 17, 20, 21, 21, 23, 23, 28, 28, 32, 33, 34, 34, 35, 35, 36, 39, 39, 40, 41, 41, 42, 44, 46, 47, 48, 49, 49<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16789\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-14.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 14\" width=\"259\" height=\"166\" \/><br \/>\nAnswer:<br \/>\nMake the stem leaf plot to find the number of text messages you received per hour.<br \/>\n40, 40, 42, 46, 46, 49, 51, 51, 53, 53, 57, 57, 57, 59, 59, 59, 61, 62, 62, 65, 65, 66, 67, 68, 68, 70, 72, 72, 73, 74.<\/p>\n<p><strong>MAKING A STEM-AND-LEAF PLOT Make a stem-and-leaf plot of the data.<\/strong><br \/>\nQuestion 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16790\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-15.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 15\" width=\"207\" height=\"106\" \/><br \/>\nAnswer:<br \/>\nWe have to write the stem and leaf plot for the above table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29092\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_9.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 10 Data Displays img_9\" width=\"236\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_9.jpg 236w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_9-150x150.jpg 150w\" sizes=\"(max-width: 236px) 100vw, 236px\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16791\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-16.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 16\" width=\"208\" height=\"105\" \/><br \/>\nAnswer:<br \/>\nWe have to write the stem and leaf plot for the above table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29093\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_10.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 10 Data Displays img_10\" width=\"236\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_10.jpg 236w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_10-150x150.jpg 150w\" sizes=\"(max-width: 236px) 100vw, 236px\" \/><\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16792\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-17.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 17\" width=\"208\" height=\"104\" \/><br \/>\nAnswer:<br \/>\nWe have to write the stem and leaf plot for the above table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29107\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_10-1.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 10 Data Displays img_10\" width=\"236\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_10-1.jpg 236w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_10-1-150x150.jpg 150w\" sizes=\"(max-width: 236px) 100vw, 236px\" \/><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16793\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-18.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 18\" width=\"209\" height=\"106\" \/><br \/>\nAnswer:<br \/>\nWe have to write the stem and leaf plot for the above table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29109\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_12.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 10 Data Displays img_12\" width=\"236\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_12.jpg 236w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_12-150x150.jpg 150w\" sizes=\"(max-width: 236px) 100vw, 236px\" \/><\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16794\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-19.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 19\" width=\"204\" height=\"103\" \/><br \/>\nAnswer:<br \/>\nWe have to write the stem and leaf plot for the above table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29111\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_13.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 10 Data Displays img_13\" width=\"236\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_13.jpg 236w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_13-150x150.jpg 150w\" sizes=\"(max-width: 236px) 100vw, 236px\" \/><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16795\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-20.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 20\" width=\"200\" height=\"103\" \/><br \/>\nAnswer:<br \/>\nWe have to write the stem and leaf plot for the above table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29122\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_14.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 10 Data Displays img_14\" width=\"236\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_14.jpg 236w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_14-150x150.jpg 150w\" sizes=\"(max-width: 236px) 100vw, 236px\" \/><\/p>\n<p>Question 21.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend makes a stem-and-leaf plot of the data. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16796\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-21.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 21\" width=\"198\" height=\"154\" \/><br \/>\n51, 25, 47, 42, 55, 26, 50, 44, 55<br \/>\nAnswer: your friend is correct<\/p>\n<p>Explanation:<br \/>\nIn stem and leaf plot the tens place represent stem and the ones place represent the leaf.<\/p>\n<p><strong>MODELING REAL LIFE<\/strong><br \/>\nThe stem-and-leaf plot shows the numbers of confirmed cases of a virus in 15 countries.<br \/>\nQuestion 22.<br \/>\nHow many of the countries have more than 60 confirmed cases?<br \/>\nAnswer: 6 countries<\/p>\n<p>Explanation:<br \/>\nBy seeing the above stem and leaf plot we can find the number of cases more than 60.<br \/>\nThe number of leaf represents the number of countries.<br \/>\n62, 63, 63, 67, 75, 97.<br \/>\nThus there are 6 countries that have more than 60 confirmed cases.<\/p>\n<p>Question 23.<br \/>\nFind the mean, median, mode, range, and interquartile range of the data.<br \/>\nAnswer:<br \/>\n41, 41, 43, 43, 45, 50, 52, 53, 54, 62, 63, 63, 67, 75, 97<br \/>\nIn its simplest mathematical definition regarding data sets, the mean used is the arithmetic mean, also referred to as mathematical expectation, or average.<br \/>\nMean:<br \/>\nmean = (41+41+43+43+45+50+52+53+54+62+63+63+67+75+97)\/15<br \/>\nmean = 56.6<br \/>\nMedian:<br \/>\nIn the odd cases where there are only two data samples or there is an even number of samples where all the values are the same, the mean and median will be the same.<br \/>\n41, 41, 43, 43, 45, 50, 52, <strong>53<\/strong>, 54, 62, 63, 63, 67, 75, 97<br \/>\nSo, the median of the given data is 53.<br \/>\nMode:<br \/>\nThe mode is the value in a data set that has the highest number of recurrences.<br \/>\n41, 41, 43, 43, 45, 50, 52, 53, 54, 62, 63, 63, 67, 75, 97<br \/>\nmode = 41, 43, 63 (Repeated 2 times)<\/p>\n<p>Question 24.<br \/>\nHow are the data distributed?<br \/>\nAnswer:<br \/>\nThe distribution of a data set is the shape of the graph when all possible values are plotted on a frequency graph. Usually, we are not able to collect all the data for our variable of interest.<\/p>\n<p>Question 25.<br \/>\nWhich data value is an outlier? Describe how the outlier affects the mean.<br \/>\nAnswer:<br \/>\nOutliers affect the mean value of the data but have little effect on the median or mode of a given set of data.<br \/>\nExample: A student receives a zero on a quiz and subsequently. has the following scores: 0, 70, 70, 80, 85, 90, 90, 90, 95, 100. Outlier: 0.<\/p>\n<p>Question 26.<br \/>\n<strong>REASONING<\/strong><br \/>\nEach stem-and-leaf plot below has a mean of 39. Without calculating, determine which stem-and-leaf plot has the lesser mean absolute deviation. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16798\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-23.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 23\" width=\"390\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-23.png 390w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-23-300x104.png 300w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/><br \/>\nAnswer:<br \/>\ni. 23, 27, 30, 32, 36, 39, 41, 42, 45, 48, 51, 54<br \/>\nMean = (23+27+30+32+36+39+41+42+45+48+51+54)\/12<br \/>\nMean = 39<br \/>\nThe mean absolute deviation is 7.833<br \/>\nii. 22, 24, 25, 28, 29, 33, 38, 45, 53, 56, 57, 58<br \/>\nMean = (22+24+25+28+29+33+38+45+53+56+57+58)\/12<br \/>\nMean = 39<br \/>\nThe mean absolute deviation is 12.333<br \/>\nThus the first stem and leaf plot has the lesser mean absolute deviation.<\/p>\n<p>Question 27.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe stem-and-leaf plot shows the daily high temperatures (in degrees Fahrenheit) for the first 15 days of June.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16799\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-24.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 24\" width=\"195\" height=\"121\" \/><br \/>\na. When you include the daily high temperatures for the rest of the month, the mean absolute deviation increases. Draw a stem-and-leaf plot that could represent all of the daily high temperatures for the month.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29559\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-12-Data-Displays-img_6.jpg\" alt=\"Big Ideas Math Answers Grade 6 Chapter 12 Data Displays img_6\" width=\"236\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-12-Data-Displays-img_6.jpg 236w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-12-Data-Displays-img_6-150x150.jpg 150w\" sizes=\"(max-width: 236px) 100vw, 236px\" \/><br \/>\nb. Use your stem-and-leaf plot from part(a) to answer the question, \u201cWhat is a typical daily high temperature in June?\u201d<br \/>\nAnswer: 89\u00b0F is the high temperature in the month of June.<\/p>\n<p>Question 28.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nThe back-to-back stem-and-leaf plot shows the 9-hole golf scores for two golfers. Only one of the golfers can compete in a tournament as your teammate. Use measures of center and measures of variation to support choosing either golfer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16800\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.1-25.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.1 25\" width=\"298\" height=\"121\" \/><br \/>\nAnswer:<br \/>\nThe scores of Rich are<br \/>\n35, 37, 41, 42, 43, 44, 45, 48<br \/>\nThe scores of Will are<br \/>\n42, 43, 44, 44, 46, 47, 47, 48, 49<br \/>\nWill can compete in the tournament.<\/p>\n<h3><a id=\"Lesson_10.2_Histograms\"><\/a>Lesson 10.2 Histograms<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Performing an Experiment<br \/>\nWork with a partner.<br \/>\na. Make the airplane shown from a single sheet of 8\\(\\frac{1}{2}\\) by-11-inch paper. Then design and make your own paper airplane.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16801\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-1.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 1\" width=\"652\" height=\"616\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-1.png 652w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-1-300x283.png 300w\" sizes=\"(max-width: 652px) 100vw, 652px\" \/><br \/>\nb. <strong>PRECISION<\/strong><br \/>\nFly each airplane 20 times. Keep track of the distance flown each time. Specify Units. What units will you use to measure the distance flown? Will the units you use affect the results in your frequency table? Explain.<br \/>\nc. A frequency table groups data values into intervals. The frequency is the number of values in an interval. Use a frequency table to organize the results for each airplane.<br \/>\nd. <strong>MODELING<\/strong> Represent the data in the frequency tables graphically. Which airplane flies farther? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-16802\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-3.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 3\" width=\"186\" height=\"118\" \/><\/p>\n<p><strong>Key Idea<\/strong><br \/>\nHistograms<br \/>\np. 463 frequency, A histogram is a bar graph that shows the frequencies of data values in intervals of the same size.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16803\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-4.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 4\" width=\"254\" height=\"162\" \/><br \/>\nThe height of a bar represents the frequency of the values in the interval.<\/p>\n<p><strong>EXAMPLE 1<\/strong><br \/>\nMaking a Histogram<br \/>\nThe frequency table shows the numbers of laps that people in a swimming class completed today. Display the data in a histogram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16804\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-5.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 5\" width=\"225\" height=\"175\" \/><br \/>\nStep 1: Draw and label the axes.<br \/>\nStep 2: Draw a bar to represent the frequency of each interval.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16805\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-6.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 6\" width=\"471\" height=\"182\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-6.png 471w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-6-300x116.png 300w\" sizes=\"(max-width: 471px) 100vw, 471px\" \/><\/p>\n<p><strong>Try It<br \/>\n<\/strong>Question 1.<br \/>\nThe frequency table shows the ages of people riding a roller coaster. Display the data in a histogram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16806\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-7.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 7\" width=\"398\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-7.png 398w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-7-300x50.png 300w\" sizes=\"(max-width: 398px) 100vw, 398px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-29843\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answers-Chapter-10-Data-Displays-img_21-300x229.jpg\" alt=\"BIM Grade 6 Answers Chapter 10 Data Displays img_21\" width=\"300\" height=\"229\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answers-Chapter-10-Data-Displays-img_21-300x229.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answers-Chapter-10-Data-Displays-img_21.jpg 400w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>EXAMPLE 2<\/strong><br \/>\nUsing a Histogram<br \/>\nThe histogram shows winning speeds at the Daytona 500.<br \/>\n(a) Which interval contains the most data values?<br \/>\n(b) How many of the winning speeds are less than 140 miles per hour?<br \/>\n(c) How many of the winning speeds are at least 160 miles per hour?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16807\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-8.1.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 8.1\" width=\"365\" height=\"180\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-8.1.png 365w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-8.1-300x148.png 300w\" sizes=\"(max-width: 365px) 100vw, 365px\" \/><br \/>\na. The interval with the tallest bar contains the most data values.<br \/>\nSo, the 150\u2212159 miles per hour interval contains the most data values.<br \/>\nb. One winning speed is in the 120\u2212129 miles per hour interval, and eight winning speeds are in the 130\u2212139 miles per hour interval.<br \/>\nSo, 1 + 8 = 9 winning speeds are less than 140 miles per hour.<br \/>\nc. Eight winning speeds are in the 160\u2212169 miles per hour interval, and five winning speeds are in the 170\u2212179 miles per hour interval.<br \/>\nSo, 8 + 5 =13 winning speeds are at least 160 miles per hour.<\/p>\n<p><strong>Try It<\/strong><br \/>\nQuestion 2.<br \/>\nThe histogram shows the numbers of hours that students in a class slept last night.<br \/>\na. How many students slept at least 8 hours?<br \/>\nb. How many students slept less than 12 hours?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16808\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-8.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 8\" width=\"513\" height=\"166\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-8.png 513w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-8-300x97.png 300w\" sizes=\"(max-width: 513px) 100vw, 513px\" \/><\/p>\n<p>Answer:<\/p>\n<p>A. Number of students who slept for 8 to 11 hours is 8.<br \/>\nNumber of students who slept for 12 to 15 hours is 3.<br \/>\nThe total number of students who slept for atleast 8 hours is 8.<\/p>\n<p>B. Number of students who slept for 8 to 11 hours is 8.<br \/>\nNumber of students who slept for 4 to 7 hours is 8.<br \/>\nNumber of students who slept for 0 to 3 hours is 2.<br \/>\nThus the number of students who slept for less than 12 hours is 8 + 8 + 2 = 18 students<\/p>\n<p><strong>EXAMPLE 3<\/strong><br \/>\nComparing Data Displays<br \/>\nThe data displays show how many push-ups students in a class completed for a physical fitness test. Which data display can you use to find how many students are in the class? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16809\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-9.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 9\" width=\"526\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-9.png 526w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-9-300x106.png 300w\" sizes=\"(max-width: 526px) 100vw, 526px\" \/><br \/>\nYou can use the histogram because it shows the number of students in each interval. The sum of these values represents the number of students in the class. You cannot use the circle graph because it does not show the number of students in each interval.<\/p>\n<p><strong>Try It<\/strong><br \/>\nQuestion 3.<br \/>\nWhich data display should you use to describe the portion of the entire class that completed 30\u221239 push-ups? Explain.<br \/>\nAnswer: You should use the percentage of the number of students in the interval of 30-39 to find the completed push-ups.<br \/>\nThe portion of the entire class that completed 30\u221239 push-ups is 24%<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal<br \/>\nQuestion 4.<br \/>\n<strong>MAKING A HISTOGRAM<\/strong><br \/>\nThe table shows the numbers of siblings of students in a class.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16810\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-10.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 10\" width=\"156\" height=\"176\" \/><br \/>\na. Display the data in a histogram.b. Explain how you chose reasonable intervals for your histogram in part<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nCan you find the range and the interquartile range of the data in the histogram? If so, find them. If you cannot find them, explain why not.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16811\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-11.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 11\" width=\"212\" height=\"169\" \/><br \/>\nAnswer:<\/p>\n<p><strong>EXAMPLE 4<\/strong><br \/>\nModeling Real Life made using the data displays in Example 3?<br \/>\nA. Twelve percent of the class completed 9 push-ups.<br \/>\nB. Five students completed at least 10 and at most 19 push-ups.<br \/>\nC. At least one student completed more than 39 push-ups.<br \/>\nD. Less than \\(\\frac{1}{4}\\) of the class completed 30 or more push-ups.<br \/>\nThe circle graph shows that12% completed 0\u22129 push-ups, but you cannot determine how many completed exactly 9. So, Statement A cannot be made.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16812\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-12.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 12\" width=\"235\" height=\"203\" \/><br \/>\nIn the histogram, the bar height for the 10\u221219 interval is 5, and the bar height for the 40\u221249 interval is 1. So, Statements B and C can be made.<br \/>\nThe circle graph shows that24% completed 30\u221239 push-ups, and 4% completed 40\u221249 push-ups. So, 24% + 4% =28% completed 30 or more push-ups. Because \\(\\frac{1}{4}\\) = 25% and 28% &gt; 25%, Statement D cannot be made.<br \/>\nThe correct answers are A and D.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16813\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-13.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 13\" width=\"238\" height=\"189\" \/><br \/>\nQuestion 6.<br \/>\nThe histogram shows the numbers of rebounds per game for a middle school basketball player in a season.<br \/>\na. Which interval contains the most data values?<br \/>\nb. 54 How many games did the player play during the season?<br \/>\nc. In what percent of the games did the player have 4 or more rebounds?<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nDetermine whether you can make each statement by using the histogram in the previous exercise.Explain.Rebounds<br \/>\na. The basketball player had 2 rebounds in 6 different games.<br \/>\nb. The basketball player had more than 1 rebound in 9 different games<br \/>\nAnswer:<\/p>\n<h3><a id=\"Histograms_Homework_&amp;_Practice_10.2\"><\/a>Histograms Homework &amp; Practice 10.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Make a stem-and-leaf plot of the data.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16814\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-14.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 14\" width=\"170\" height=\"106\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29766\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-img_11.jpg\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays img_11\" width=\"236\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-img_11.jpg 236w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-img_11-150x150.jpg 150w\" sizes=\"(max-width: 236px) 100vw, 236px\" \/><\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16815\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-15.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 15\" width=\"194\" height=\"107\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29771\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-img_12.jpg\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays img_12\" width=\"236\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-img_12.jpg 236w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-img_12-150x150.jpg 150w\" sizes=\"(max-width: 236px) 100vw, 236px\" \/><\/p>\n<p><strong>Find the percent of the number.<\/strong><br \/>\nQuestion 3.<br \/>\n25% of 180<br \/>\nAnswer: 45<\/p>\n<p>Explanation:<br \/>\n25% = 25\/100<br \/>\n25\/100 \u00d7 180<br \/>\nWe get 45<br \/>\nSo, 25% of 180 is 45.<\/p>\n<p>Question 4.<br \/>\n30% of 90<br \/>\nAnswer: 27<\/p>\n<p>Explanation:<br \/>\n30% = 30\/100<br \/>\n30\/100 \u00d7 90 = 27<br \/>\nSo, 30% of 90 is 27<\/p>\n<p>Question 5.<br \/>\n16% of 140<br \/>\nAnswer: 22.4<\/p>\n<p>Explanation:<br \/>\n16% = 16\/100<br \/>\n16\/100 \u00d7 140 = 22.4<br \/>\nSo, 16% of 140 is 22.4<\/p>\n<p>Question 6.<br \/>\n64% of 807.<br \/>\nAnswer: 516.48<\/p>\n<p>Explanation:<br \/>\n64% = 64\/100<br \/>\n64\/100 \u00d7 807 = 516.48<br \/>\nSo, 64% of 807 is 516.48<\/p>\n<p>Question 7.<br \/>\nWhat is the least common multiple of 7 and 12?<br \/>\nA. 28<br \/>\nB. 42<br \/>\nC. 84<br \/>\nD. 168<br \/>\nAnswer: 84<\/p>\n<p>Explanation:<br \/>\nFind and list multiples of each number until the first common multiple is found. This is the lowest common multiple.<br \/>\nMultiples of 7:<br \/>\n7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98<br \/>\nMultiples of 12:<br \/>\n12, 24, 36, 48, 60, 72, 84, 96, 108<br \/>\nTherefore,<br \/>\nLCM(7, 12) = 84<br \/>\nThus the correct answer is option c.<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\nMAKING A FREQUENCY TABLE Organize the data using a frequency table. (See Exploration 1, p. 463.)<br \/>\nQuestion 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16816\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-16.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 16\" width=\"189\" height=\"103\" \/><br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-29779\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_13.jpg\" alt=\"BIM Grade 6 Answer Key Chapter 10 Data Displays img_13\" width=\"236\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_13.jpg 236w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_13-150x150.jpg 150w\" sizes=\"(max-width: 236px) 100vw, 236px\" \/><\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16817\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-17.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 17\" width=\"224\" height=\"102\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29795\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_14.jpg\" alt=\"BIM Grade 6 Answer Key Chapter 10 Data Displays img_14\" width=\"236\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_14.jpg 236w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_14-150x150.jpg 150w\" sizes=\"(max-width: 236px) 100vw, 236px\" \/><\/p>\n<p><strong>MAKING A HISTOGRAM Display the data in a histogram.<\/strong><br \/>\nQuestion 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16818\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-18.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 18\" width=\"151\" height=\"146\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-29800\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_15-300x211.jpg\" alt=\"BIM Grade 6 Answer Key Chapter 10 Data Displays img_15\" width=\"300\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_15-300x211.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_15.jpg 352w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16819\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-19.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 19\" width=\"150\" height=\"151\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-29803\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_16-300x211.jpg\" alt=\"BIM Grade 6 Answer Key Chapter 10 Data Displays img_16\" width=\"300\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_16-300x211.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_16.jpg 352w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16820\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-20.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 20\" width=\"154\" height=\"153\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-20.png 154w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-20-150x150.png 150w\" sizes=\"(max-width: 154px) 100vw, 154px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-29817\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_17-300x211.jpg\" alt=\"BIM Grade 6 Answer Key Chapter 10 Data Displays img_17\" width=\"300\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_17-300x211.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_17.jpg 352w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16821\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-21.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 21\" width=\"152\" height=\"148\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-29822\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_18-300x211.jpg\" alt=\"BIM Grade 6 Answer Key Chapter 10 Data Displays img_18\" width=\"300\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_18-300x211.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_18.jpg 352w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16822\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-22.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 22\" width=\"155\" height=\"184\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-29824\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_19-300x211.jpg\" alt=\"BIM Grade 6 Answer Key Chapter 10 Data Displays img_19\" width=\"300\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_19-300x211.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_19.jpg 352w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-23.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 23\" width=\"184\" height=\"173\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-29831\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_20-300x173.jpg\" alt=\"BIM Grade 6 Answer Key Chapter 10 Data Displays img_20\" width=\"300\" height=\"173\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_20-300x173.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_20.jpg 431w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 16.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend displays the data in a histogram. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16824\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-24.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 24\" width=\"465\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-24.png 465w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-24-300x114.png 300w\" sizes=\"(max-width: 465px) 100vw, 465px\" \/><br \/>\nAnswer: yes your friend is correct.<br \/>\nThe frequency table matches the histogram.<\/p>\n<p>Question 17.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe histogram shows the numbers of magazines read last month by the students in a class.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16825\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-25.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 25\" width=\"294\" height=\"180\" \/><br \/>\na. Which interval contains the fewest data values?<br \/>\nAnswer: The interval 4-5 has the fewest data values.<br \/>\nb. How many students are in the class?<br \/>\nAnswer:<br \/>\n0-1 = 2<br \/>\n2-3 = 15<br \/>\n4-5 = 0<br \/>\n6-7 = 3<br \/>\n2 + 15 + 3 = 20<br \/>\nc. What percent of the students read fewer than six magazines?<br \/>\nAnswer: By seeing the above histogram we can say that 25% of the students read fewer than six magazines.<\/p>\n<p>Question 18.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend interprets the histogram. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16826\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-26.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 26\" width=\"554\" height=\"199\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-26.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-26-300x108.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><br \/>\nAnswer:<br \/>\nCompare your friend with the above histogram.<br \/>\nBy seeing the above histogram we can say that it took 12 seconds to download songs.<br \/>\nSo, your friend is correct.<\/p>\n<p>Question 19.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe histogram shows the percent of the voting-age population in each state who voted in a presidential election. Explain whether the graph supports each statement.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16827\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-27.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 27\" width=\"363\" height=\"183\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-27.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-27-300x151.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><br \/>\na. Only 40% of one state voted.<br \/>\nb. In most states, between 50% and 64.9% voted.<br \/>\nc. The mode of the data is between 55% and 59.9%<br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe histograms show the areas of counties in Pennsylvania and Indiana. Which state do you think has the greater area? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-28.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 28\" width=\"570\" height=\"207\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-28.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-28-300x109.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe data displays show how many pounds of garbage apartment residents produced in 1 week. Which data display can you use to find how many residents produced more than 25 pounds of garbage? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-29.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 29\" width=\"547\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-29.png 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-29-300x97.png 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 22.<br \/>\n<strong>REASONING<\/strong><br \/>\nDetermine whether you can make each statement by using the data displays in Exercise 21. Explain your reasoning.<br \/>\na. One resident produced 10 pounds of garbage.<br \/>\nb. Twelve residents produced between 20 and 29 pounds of garbage.<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe table shows the lengths of some whales in a marine sanctuary.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16830\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-30.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays 10.2 30\" width=\"444\" height=\"220\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-30.png 444w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-10.2-30-300x149.png 300w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><br \/>\na. Make a histogram of the data starting with the interval 51\u221255.<br \/>\nb. Make another histogram of the data using a different-sized interval.<br \/>\nc. Compare and contrast the two histograms.<br \/>\nAnswer:<\/p>\n<p>Question 24.<br \/>\n<strong>LOGIC<\/strong><br \/>\nCan you find the mean or the median of the data in Exercise 17? Explain.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_10.3_Shapes_of_Distributions\"><\/a>Lesson 10.3 Shapes of Distributions<\/h3>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-16831\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 1\" width=\"660\" height=\"212\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-1.png 660w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-1-300x96.png 300w\" sizes=\"(max-width: 660px) 100vw, 660px\" \/><\/p>\n<p><strong>EXPLORATION<\/strong><br \/>\nDescribing Shapes of Distributions<br \/>\nWork with a partner. The lists show the first three digits and last four digits of several phone numbers in the contact list of a cell phone.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16832\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-2.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 2\" width=\"591\" height=\"238\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-2.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-2-300x121.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><br \/>\na. Compare and contrast the distribution of the last digit of each phone number to the distribution of the first digit of each phone number. Describe the shapes of the distributions.<br \/>\nb. Describe the shape of the distribution of the data in the table below. Compare it to the distributions in part(a).<br \/>\nAnswer:<\/p>\n<p>You can use dot plots and histograms to identify shapes of distributions.<\/p>\n<p><strong>Key Ideas<\/strong><br \/>\nSymmetric and Skewed Distributions<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16833\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-3.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 3\" width=\"696\" height=\"248\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-3.png 696w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-3-300x107.png 300w\" sizes=\"(max-width: 696px) 100vw, 696px\" \/><\/p>\n<p><strong>EXAMPLE 1<\/strong><br \/>\nDescribing Shapes of Distributions<\/p>\n<p>Describe the shape of each distribution.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16834\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-4.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 4\" width=\"479\" height=\"279\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-4.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-4-300x175.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/p>\n<p><strong>Try It<\/strong><br \/>\nQuestion 1.<br \/>\nDescribe the shape of the distribution.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16835\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-5.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 5\" width=\"230\" height=\"144\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-28308\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/BIM-6th-Grade-Chapter-10-Data-Displays-Answer-Key-img_4-300x218.jpg\" alt=\"BIM 6th Grade Chapter 10 Data Displays Answer Key img_4\" width=\"300\" height=\"218\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/BIM-6th-Grade-Chapter-10-Data-Displays-Answer-Key-img_4-300x218.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/BIM-6th-Grade-Chapter-10-Data-Displays-Answer-Key-img_4.jpg 396w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nA symmetric distribution has a graph in which the left side is a mirror image of the right side.<br \/>\nA skewed distribution has a graph in which a \u201ctail\u201d extends to the left and most data are on the right OR a \u201ctail\u201d extends to the right and most data are on the left.<\/p>\n<p><strong>EXAMPLE 2<\/strong><br \/>\nDescribing the Shape of a Distribution<br \/>\nThe frequency table shows the ages of people watching a comedy in a theater. Display the data in a histogram. Then describe the shape of the distribution.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16836\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-6.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 6\" width=\"507\" height=\"226\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-6.png 507w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-6-300x134.png 300w\" sizes=\"(max-width: 507px) 100vw, 507px\" \/><br \/>\nDraw and label the axes. Then draw a bar to represent the frequency of each interval.<br \/>\nMost of the data are on the right, and the tail extends to the left.<br \/>\nSo, the distribution is skewed left.<br \/>\nAnswer:<br \/>\nFor a distribution that is skewed right, the tail extends to the right and most of the data are on the left side of the graph.<\/p>\n<p><strong>Try It<\/strong><br \/>\nQuestion 2.<br \/>\nThe frequency table shows the ages of people watching a historical movie in a theater. Display the data in a histogram. Describe the shape of the distribution.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16837\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-7.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 7\" width=\"414\" height=\"69\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-7.png 414w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-7-300x50.png 300w\" sizes=\"(max-width: 414px) 100vw, 414px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<br \/>\nQuestion 3.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain in your own words what it means for a distribution to be (a) skewed left, (b) symmetric, and (c) skewed right.<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n<strong>DESCRIBING A DISTRIBUTION<\/strong><br \/>\nDisplay the data shown in a histogram. Describe the shape of the distribution.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16838\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-8.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 8\" width=\"167\" height=\"180\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich histogram does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16839\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-9.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 9\" width=\"454\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-9.png 454w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-9-300x68.png 300w\" sizes=\"(max-width: 454px) 100vw, 454px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>EXAMPLE 3<\/strong><br \/>\nModeling Real Life<br \/>\nThe histogram shows the ages of people watching an animated movie in the same theater as in Example 2. Which movie has an older audience?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16840\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-10.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 10\" width=\"226\" height=\"187\" \/><br \/>\nUnderstand the problem<br \/>\nYou are given histograms that display the ages of people watching two movies. You are asked to determine which movie has an older audience.<\/p>\n<p>Make a plan<br \/>\nUse the intervals and distributions of the data to determine which movie has an older audience.<\/p>\n<p>Solve and check<br \/>\nThe intervals in the histograms are the same. Most of the data for the animated movie are on the left, while most of the data for the comedy are on the right. This means that the people watching the comedy are generally older than the people watching the animated movie.<\/p>\n<p>So, the comedy has an older audience.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16841\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-11.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 11\" width=\"167\" height=\"219\" \/><br \/>\nCheck Reasonableness<br \/>\nThe movies have similar attendance. However,only4 people watching the comedy are 17 or under. A total of 35 people watching the animated movie are 17 or under. So, it is reasonable to conclude that the comedy has an older audience.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<br \/>\nQuestion 6.<br \/>\nThe frequency table shows the numbers of visitors each day to parks in Aurora and Grover in one month. Which park generally has more daily visitors? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16842\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-12.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 12\" width=\"193\" height=\"163\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe frequency tables below show the ages of guests on two cruises. Can you make accurate comparisons of the ages of the guests? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16843\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-13.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 13\" width=\"363\" height=\"156\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-13.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-13-300x129.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Shapes_of_Distributions_Homework_&amp;_Practice_10.3\"><\/a>Shapes of Distributions Homework &amp; Practice 10.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Display the data in a histogram.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16844\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-14.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 14\" width=\"143\" height=\"148\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-28297\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-12-Data-Displays-img_1-300x223.jpg\" alt=\"Big Ideas Math Answers Grade 6 Chapter 12 Data Displays img_1\" width=\"300\" height=\"223\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-12-Data-Displays-img_1-300x223.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-12-Data-Displays-img_1.jpg 396w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nOn the vertical axis, place frequencies. Label this axis &#8220;Frequency&#8221;.<br \/>\nOn the horizontal axis, place the lower value of each interval.<br \/>\nDraw a bar extending from the lower value of each interval to the lower value of the next interval.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16845\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-15.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 15\" width=\"170\" height=\"145\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-28299\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_2-300x218.jpg\" alt=\"BIM Grade 6 Answer Key Chapter 10 Data Displays img_2\" width=\"300\" height=\"218\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_2-300x218.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/BIM-Grade-6-Answer-Key-Chapter-10-Data-Displays-img_2.jpg 396w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>On the vertical axis, place frequencies. Label this axis &#8220;Frequency&#8221;.<br \/>\nOn the horizontal axis, place the lower value of each interval.<br \/>\nDraw a bar extending from the lower value of each interval to the lower value of the next interval.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16846\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-16.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 16\" width=\"178\" height=\"148\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-28301\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-12-Data-Displays-img_3-300x242.jpg\" alt=\"Big Ideas Math Answers Grade 6 Chapter 12 Data Displays img_3\" width=\"300\" height=\"242\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-12-Data-Displays-img_3-300x242.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-12-Data-Displays-img_3.jpg 396w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>On the vertical axis, place frequencies. Label this axis &#8220;Frequency&#8221;.<br \/>\nOn the horizontal axis, place the lower value of each interval.<br \/>\nDraw a bar extending from the lower value of each interval to the lower value of the next interval.<\/p>\n<p><strong>Write a unit rate for the situation.<\/strong><br \/>\nQuestion 4.<br \/>\n$200 per 8 days<br \/>\nAnswer:<br \/>\n200\/8 = 25<br \/>\nThus $25 per day.<\/p>\n<p>Question 5.<br \/>\n60 kilometers for every 1.5 hours<br \/>\nAnswer:<br \/>\nYour average speed is 60 km per 1.5 hours.<br \/>\n60\/1.5 = 40 km\/hr<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p>DESCRIBING SHAPES OF DISTRIBUTIONS Describe the shape of the distribution of the data in the table. (See Exploration 1, p. 471.)<br \/>\nQuestion 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16847\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-17.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 17\" width=\"239\" height=\"82\" \/><br \/>\nAnswer:<br \/>\nStep 1:<br \/>\nOrder the data<br \/>\n0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16848\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-18.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 18\" width=\"232\" height=\"83\" \/><br \/>\nAnswer:<br \/>\nStep 1:<br \/>\nOrder the data<br \/>\n12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16.<\/p>\n<p><strong>DESCRIBING SHAPES OF DISTRIBUTIONS<\/strong><\/p>\n<p><strong>Describe the shape of the distribution.<\/strong><br \/>\nQuestion 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16849\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-19.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 19\" width=\"223\" height=\"142\" \/><br \/>\nAnswer: 25, 26, 27, 27, 28, 28, 28, 28, 29, 29, 29, 29, 29, 30, 30, 30<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16850\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-20.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 20\" width=\"227\" height=\"131\" \/><br \/>\nAnswer:<\/p>\n<p>15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 20, 20, 21<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16851\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-21.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 21\" width=\"222\" height=\"189\" \/><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16852\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-22.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 22\" width=\"228\" height=\"190\" \/><br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe frequency table shows the years of experience for the medical states in Jones County and Pine County. Display the data for each county in a histogram. Which county\u2019s medical state has less experience? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16853\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-23.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 23\" width=\"591\" height=\"203\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-23.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-23-300x103.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhat is the shape of the distribution of the restaurant waiting times? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16854\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-24.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 24\" width=\"224\" height=\"184\" \/><br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\n<strong>LOGIC<\/strong><br \/>\nAre all distributions either approximately symmetric or skewed? Explain. If not, give an example.<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n<strong>REASONING<\/strong><br \/>\nCan you use a stem-and-leaf plot to describe the shape of a distribution? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe table shows the donation amounts received by a charity in one day.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16855\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-25.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 25\" width=\"520\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-25.png 520w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-25-300x70.png 300w\" sizes=\"(max-width: 520px) 100vw, 520px\" \/><br \/>\na. Make a histogram of the data starting with the interval 0\u201314. Describe the shape of the distribution.<br \/>\nb. A company adds $5 to each donation. Make another histogram starting with the same interval as in part(a). Compare the shape of this distribution with the distribution in part(a). Explain any differences in the distributions.<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nDescribe the shape of the distribution of each bar graph. Match the letters A, B, and C with the mean, the median, and the mode of each data set. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16856\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-26.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays 10.3 26\" width=\"591\" height=\"115\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-26.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-10.3-26-300x58.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_10.4_Choosing_Appropriate_Measures\"><\/a>Lesson 10.4 Choosing Appropriate Measures<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\nUsing Shapes of Distributions<br \/>\nWork with a partner.<br \/>\nIn Section 10.3 Exploration 1(a), you described the distribution of the first digits of the numbers at the right. In Exploration 1(b), you described the distribution of the data set below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16857\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-1.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 1\" width=\"410\" height=\"235\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-1.png 410w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-1-300x172.png 300w\" sizes=\"(max-width: 410px) 100vw, 410px\" \/><br \/>\nWhat do you notice about the measures of center, measures of variation, and the shapes of the distributions? Explain.<br \/>\nb. Which measure of center best describes each data set? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16858\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-2.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 2\" width=\"516\" height=\"187\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-2.png 516w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-2-300x109.png 300w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/><br \/>\nc. which measures best describe the data. Which measure of variation best describes each data set? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>You can use a measure of center and a measure of variation to describe the distribution of a data set.\ue03be shape of the distribution can help you choose which measures are the most appropriate to use.<\/p>\n<p><strong>Key Idea<\/strong><\/p>\n<p>Choosing Appropriate Measures<br \/>\nThe mean absolute deviation (MAD) uses the mean in its calculation. So, when a data distribution is symmetric,<br \/>\n\u2022 use the mean to describe the center and<br \/>\n\u2022 use the MAD to describe the variation.<\/p>\n<p>The interquartile range (IQR) uses quartiles in its calculation. So, when a data distribution is skewed,<br \/>\n\u2022 use the median to describe the center and<br \/>\n\u2022 use the IQR to describe the variation.<\/p>\n<p><strong>EXAMPLE 1<\/strong><br \/>\nChoosing Appropriate Measures<br \/>\nThe frequency table shows the number of states that border each state in the United States. What are the most appropriate measures to describe the center and the variation?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16859\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-3.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 3\" width=\"495\" height=\"317\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-3.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-3-300x192.png 300w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><br \/>\nTo see the distribution of the data, display the data in a histogram.<br \/>\nThe left side of the graph is approximately a mirror image of the right side of the graph. The distribution is symmetric.<br \/>\nSo, the mean and the mean absolute deviation are the most appropriate measures to describe the center and the variation.<\/p>\n<p><strong>Try It<\/strong><br \/>\nQuestion 1.<br \/>\nThe frequency table shows the gas mileages of several motorcycles made by a company. What are the most appropriate measures to describe the center and the variation?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16860\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-4.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 4\" width=\"415\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-4.png 415w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-4-300x59.png 300w\" sizes=\"(max-width: 415px) 100vw, 415px\" \/><br \/>\nAnswer:<br \/>\nTo see the distribution of the data, display the data in a histogram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32395\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_15-300x229.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 10 Data Displays img_15\" width=\"300\" height=\"229\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_15-300x229.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-10-Data-Displays-img_15.jpg 400w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>EXAMPLE 2<\/strong><br \/>\nDescribing a Data Set<br \/>\nThe dot plot shows the average numbers of hours students in a class sleep each night. Describe the center and the variation of the data set.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16861\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-5.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 5\" width=\"439\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-5.png 439w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-5-300x77.png 300w\" sizes=\"(max-width: 439px) 100vw, 439px\" \/><br \/>\nMost of the data values are on the right, clustered around 9, and the tail extends to the left. The distribution is skewed left, so the median and the interquartile range are the most appropriate measures to describe the center and the variation.<br \/>\nThe median is 8.5 hours. The first quartile is 7.5, and the third quartile is 9. So, the interquartile range is 9 \u2212 7.5 = 1.5 hours.<br \/>\nThe data are centered around 8.5 hours. The middle half of the data varies by no more than 1.5 hours.<\/p>\n<p><strong>Try It<\/strong><br \/>\nQuestion 2.<br \/>\nThe dot plot shows the numbers of hours people spent at the gym last week. Describe the center and the variation of the data set.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16862\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-6.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 6\" width=\"240\" height=\"129\" \/><br \/>\nAnswer:<br \/>\nMost of the data values are on the right, clustered around 6, and the tail extends to the left. The distribution is skewed left, so the median and the interquartile range are the most appropriate measures to describe the center and the variation.<br \/>\nThe median is 5 hours. The first quartile is 2, and the third quartile is 4.<br \/>\nSo, the interquartile range is 4 &#8211; 2 = 2 hours<br \/>\nThe data are centered around 5 hours. The middle half of the data varies by no more than 2 hours.<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<br \/>\nQuestion 3.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nConstruct a dot plot for which the mean is the most appropriate measure to describe the center of the distribution.<br \/>\nAnswer:<\/p>\n<p><strong>CHOOSING APPROPRIATE MEASURES<\/strong><br \/>\nChoose the most appropriate measures to describe the center and the variation. Explain your reasoning. Then find the measures you chose.<br \/>\nQuestion 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16863\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-7.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 7\" width=\"208\" height=\"87\" \/><br \/>\nAnswer:<br \/>\n20, 28, 32, 32, 36, 36, 40, 40, 40, 40, 44, 44, 44, 48<br \/>\nOrder your data set from lowest to highest values<br \/>\nFind the median. This is the second quartile Q2.<br \/>\nAt Q2 split the ordered data set into two halves.<br \/>\nThe lower quartile Q1 is the median of the lower half of the data.<br \/>\nQ1 = 32<br \/>\nThe upper quartile Q3 is the median of the upper half of the data.<br \/>\nQ3 = 44<br \/>\nMedian is the average of the data values.<br \/>\nSo, the median, Q2 is 40.<br \/>\nInterquartile Range = Q3 &#8211; Q1<br \/>\nIQR = 44 &#8211; 32<br \/>\nIQR = 12<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16864\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-8.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 8\" width=\"213\" height=\"89\" \/><br \/>\nAnswer:<br \/>\n8, 10, 10, 12, 12, 12, 14, 14, 14, 14, 16, 16, 16, 18, 18, 20<br \/>\n8, 10, 12, 14, 16, 18, 20<br \/>\nOrder your data set from lowest to highest values<br \/>\nFind the median. This is the second quartile Q2.<br \/>\nAt Q2 split the ordered data set into two halves.<br \/>\nThe lower quartile Q1 is the median of the lower half of the data.<br \/>\nQ1 = 12<br \/>\nThe upper quartile Q3 is the median of the upper half of the data.<br \/>\nQ3 = 16<br \/>\nMedian is the average of the data values.<br \/>\nSo, the median, Q2 is 14<br \/>\nInterquartile Range = Q3 &#8211; Q1<br \/>\nIQR = 16 &#8211; 12<br \/>\nIQR = 4<\/p>\n<p>Question 6.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain why the most appropriate measures to describe the center and the variation of a data set are determined by the shape of the distribution.<br \/>\nAnswer:<br \/>\nYou can use a measure of center and a measure of variation to describe the distribution of a data set. The shape of the distribution can help you choose which measures are the most appropriate to use. The dot plot shows the average number of hours students in a class sleep each night.<\/p>\n<p><strong>EXAMPLE 3<\/strong><br \/>\nModeling Real Life<br \/>\nTwo baskets each have16 envelopes with money inside, as shown in the tables. How much does a typical envelope in each basket contain? Why might a person want to pick from Basket B instead of Basket A?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16865\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-9.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 9\" width=\"659\" height=\"268\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-9.png 659w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-9-300x122.png 300w\" sizes=\"(max-width: 659px) 100vw, 659px\" \/><br \/>\nIn each graph, the left side is a mirror image of the right side. Because both distributions are symmetric, the mean and the mean absolute deviation are the most appropriate measures to describe the center and the variation.<br \/>\nThe mean of each data set is \\(\\frac{800}{16}\\) = $50. The MAD of Basket A is \\(\\frac{320}{16}\\) = $20, and the MAD of Basket B is \\(\\frac{120}{16}\\) = $7.50. So, Basket A has more variability.<\/p>\n<p>A typical envelope in each basket contains about $50. A person may choose from Basket B instead of Basket A because there is less variability. This means it is more likely to get an amount near $50 by choosing an envelope from Basket B than by choosing an envelope from Basket A.<br \/>\nAnswer:<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<br \/>\nQuestion 7.<br \/>\nWhy might a person want to pick from Basket A instead of Basket B in Example 3? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nIn a video game, two rooms each have 12 treasure chests containing gold coins. The tables show the numbers of coins in each chest. You pick one chest and are rewarded with the coins inside. From which room would you choose? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16866\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-10.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 10\" width=\"425\" height=\"205\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-10.png 425w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-10-300x145.png 300w\" sizes=\"(max-width: 425px) 100vw, 425px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nCreate a dot plot of the numbers of pets that students in your class own. Describe the center and the variation of the data set.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Choosing_Appropriate_Measures_Homework_&amp;_practice_10.4\"><\/a>Choosing Appropriate Measures Homework &amp; Practice 10.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Describe the shape of the distribution.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16867\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-11.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 11\" width=\"217\" height=\"142\" \/><br \/>\nAnswer:<br \/>\nOrder the data<br \/>\n5, 6, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10<br \/>\nThe shape of the distribution for the above dot plot is<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32394\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-11.jpg\" alt=\"Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-11\" width=\"217\" height=\"142\" \/><\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16868\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-12.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 12\" width=\"227\" height=\"156\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Find the median, first quartile, third quartile, and interquartile range of the data.<\/strong><br \/>\nQuestion 3.<br \/>\n68, 74, 67, 72, 63, 70, 78, 64, 76<br \/>\nAnswer:<br \/>\nOrder the data<br \/>\n63, 64, 67, 68, 70, 72, 74, 76, 78<br \/>\nThe median is nothing but the average value of the data.<br \/>\n70 is the average of the data values.<br \/>\nOrder your data set from lowest to highest values<br \/>\nFind the median. This is the second quartile Q2.<br \/>\nThus the second quartile Q2 is 70.<br \/>\nAt Q2 split the ordered data set into two halves.<br \/>\nThe lower quartile Q1 is the median of the lower half of the data.<br \/>\nThus Q1 is 65.5<br \/>\nThe upper quartile Q3 is the median of the upper half of the data.<br \/>\nQ3 is 75<br \/>\nInterquartile Range IQR = 9.5<br \/>\nIf the size of the data set is odd, do not include the median when finding the first and third quartiles.<br \/>\nIf the size of the data set is even, the median is the average of the middle 2 values in the data set. Add those 2 values, and then divide by 2. The median splits the data set into lower and upper halves and is the value of the second quartile Q2.<\/p>\n<p>Question 4.<br \/>\n39, 48, 33, 24, 30, 44, 36, 41, 28, 53<br \/>\nAnswer:<br \/>\nOrder the data<br \/>\n24, 28, 30, 33, 36, 39, 41, 44, 48, 53<br \/>\nIf the size of the data set is even, the median is the average of the middle 2 values in the data set. Add those 2 values, and then divide by 2. The median splits the data set into lower and upper halves and is the value of the second quartile Q2.<br \/>\nMedian is (36+39)\/2 = 37.5<br \/>\nOrder your data set from lowest to highest values<br \/>\nFind the median. This is the second quartile Q2.<br \/>\nThus the second quartile Q2 is 37.5<br \/>\nAt Q2 split the ordered data set into two halves.<br \/>\nThe lower quartile Q1 is the median of the lower half of the data.<br \/>\nThus Q1 is 30<br \/>\nThe upper quartile Q3 is the median of the upper half of the data.<br \/>\nQ3 is 44<br \/>\nInterquartile Range IQR = 14<br \/>\nIf the size of the data set is odd, do not include the median when finding the first and third quartiles.<\/p>\n<p><strong>Divide. Write the answer in simplest form.<\/strong><br \/>\nQuestion 5.<br \/>\n4\\(\\frac{2}{5}\\) \u00f7 2<br \/>\nAnswer: 2 \\(\\frac{1}{5}\\)<\/p>\n<p>Explanation:<br \/>\nConvert any mixed numbers to fractions.<br \/>\n4\\(\\frac{2}{5}\\) = \\(\\frac{22}{5}\\)<br \/>\n\\(\\frac{22}{5}\\) \u00d7 \\(\\frac{1}{2}\\) = \\(\\frac{22}{10}\\)<br \/>\nNow convert from improper fraction to the mixed fraction.<br \/>\n\\(\\frac{22}{10}\\) = 2 \\(\\frac{1}{5}\\)<\/p>\n<p>Question 6.<br \/>\n5\\(\\frac{1}{8}\\) \u00f7 \\(\\frac{7}{8}\\)<br \/>\nAnswer: 5 \\(\\frac{6}{7}\\)<\/p>\n<p>Explanation:<br \/>\nConvert any mixed numbers to fractions.<br \/>\n5\\(\\frac{1}{8}\\) = \\(\\frac{41}{8}\\)<br \/>\n\\(\\frac{41}{8}\\) \u00f7 \\(\\frac{7}{8}\\)<br \/>\n\\(\\frac{41}{8}\\) \u00d7 \\(\\frac{8}{7}\\) = \\(\\frac{328}{56}\\)<br \/>\nNow convert from improper fraction to the mixed fraction.<br \/>\n\\(\\frac{328}{56}\\) = 5 \\(\\frac{6}{7}\\)<\/p>\n<p>Question 7.<br \/>\n2\\(\\frac{3}{7}\\) \u00f7 1\\(\\frac{1}{7}\\)<br \/>\nAnswer: 2 \\(\\frac{1}{8}\\)<\/p>\n<p>Explanation:<br \/>\nConvert any mixed numbers to fractions.<br \/>\n2\\(\\frac{3}{7}\\) = \\(\\frac{17}{7}\\)<br \/>\n1\\(\\frac{1}{7}\\) = \\(\\frac{8}{7}\\)<br \/>\n\\(\\frac{17}{7}\\) \u00f7 \\(\\frac{8}{7}\\) = \\(\\frac{119}{56}\\)<br \/>\nSimplify the fraction<br \/>\n\\(\\frac{119}{56}\\) = 2 \\(\\frac{1}{8}\\)<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{4}{5}\\) \u00f7 7\\(\\frac{1}{2}\\)<br \/>\nAnswer: \\(\\frac{8}{75}\\)<\/p>\n<p>Explanation:<br \/>\nConvert any mixed numbers to fractions.<br \/>\n7\\(\\frac{1}{2}\\) = \\(\\frac{15}{2}\\)<br \/>\n\\(\\frac{4}{5}\\) \u00f7 \\(\\frac{15}{2}\\) = \\(\\frac{8}{75}\\)<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p>USING SHAPES OF DISTRIBUTIONS<br \/>\nFind the mean and the median of the data set. Which measure of center best describes the data set? Explain your reasoning. (See Exploration 1, p. 477.)<br \/>\nQuestion 9.<br \/>\n9, 3, 7, 7, 9, 2, 8, 9, 6, 7, 8, 9<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n24, 25, 27, 27, 23, 29, 26, 26, 26, 25, 28<br \/>\nAnswer:<\/p>\n<p><strong>CHOOSING APPROPRIATE MEASURES<\/strong><br \/>\nChoose the most appropriate measures to describe the center and the variation.<br \/>\nQuestion 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16869\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-13.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 13\" width=\"241\" height=\"127\" \/><br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16870\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-14.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 14\" width=\"238\" height=\"130\" \/><br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16871\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-15.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 15\" width=\"226\" height=\"160\" \/><br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16872\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-16.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 16\" width=\"225\" height=\"155\" \/><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n<strong>DESCRIBING DATA SETS<\/strong><br \/>\nDescribe the centers and the variations of the data sets in Exercises 11 and 12.<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe frequency table shows the numbers of eggs laid by several octopi. What are the most appropriate measures to describe the center and the variation? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16873\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-17.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 17\" width=\"351\" height=\"187\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-17.png 351w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-17-300x160.png 300w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe dot plot shows the vertical jump heights (in inches) of several professional athletes. Describe the center and the variation of the data set.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16874\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-18.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 18\" width=\"183\" height=\"328\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-18.png 183w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-18-167x300.png 167w\" sizes=\"(max-width: 183px) 100vw, 183px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nDescribe a real-life situation where the median and the interquartile range are likely the best measures of center and variation to describe the data. Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou play a board game in which you draw from one of two piles of cards. Each card has a number that says how many spaces you will move your piece forward on the game board. The tables show the numbers on the cards in each pile. From which pile would you choose? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16875\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-19.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 19\" width=\"226\" height=\"234\" \/><br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe frequency table shows the numbers of words that several students can form in 1 minute using the letters P, S, E, D, A. What are the most appropriate measures to describe the center and variation? Can you find the exact values of the measures of center and variation for the data? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16876\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-20.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 20\" width=\"408\" height=\"69\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-20.png 408w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-20-300x51.png 300w\" sizes=\"(max-width: 408px) 100vw, 408px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<strong>REASONING<\/strong><br \/>\nA bag contains 20 vouchers that can be redeemed for different numbers of tokens at an arcade, as shown in the table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16877\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-10.4-21.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays 10.4 21\" width=\"156\" height=\"143\" \/><br \/>\na. Find the most appropriate measure to describe the center of the data set.<br \/>\nb. You randomly select a voucher from the bag. How many tokens are you most likely to receive? Explain.<br \/>\nc. Are your answers in parts (a) and (b) the same? Explain why or why not.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_10.5_Box_and_Whisker_Plots\"><\/a>Lesson 10.5 Box-and-Whisker Plots<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\nDrawing a Box-and-Whisker Plot<br \/>\nWork with a partner. Each student in a sixth-grade class is asked to choose a number from 1 to 20. The results are shown below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16879\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 1\" width=\"287\" height=\"175\" \/><br \/>\na. The box-and-whisker plot below represents the data set. Which part represents the box? the whiskers? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16880\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-2.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 2\" width=\"600\" height=\"151\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-2.png 600w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-2-300x76.png 300w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><br \/>\nb. What does each of the five plotted points represent?<br \/>\nc. In your own words, describe what a box-and-whisker plot is and what it tells you about a data set.<br \/>\nd. Conduct a survey in your class. Have each student write a number from 1 to 20 on a piece of paper. Collect all of the data and draw a box-and-whisker plot that represents the data. Compare the data with the box-and-whisker plot in part(a).<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-16881\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-3.1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 3.1\" width=\"190\" height=\"112\" \/><\/p>\n<p><strong>Key Idea<\/strong><br \/>\nBox-and-Whisker Plot<br \/>\nA box-and-whisker plot represents a data set along a number line by using the least value, the greatest value, and the quartiles of the data. A box-and-whisker plot shows the variability of a data set.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16882\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-3.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 3\" width=\"430\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-3.png 430w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-3-300x76.png 300w\" sizes=\"(max-width: 430px) 100vw, 430px\" \/><br \/>\nThe five numbers that make up the box-and-whisker plot are called the five-number summary of the data set.<\/p>\n<p><strong>EXAMPLE 1<\/strong><br \/>\nMaking a Box-and-Whisker Plot<br \/>\nMake a box-and-whisker plot for the ages(in years) of the spider monkeys at a zoo.<br \/>\n15, 20, 14, 38, 30, 36, 30, 30, 27, 26, 33, 35<br \/>\nStep 1: Order the data. Find the quartiles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16883\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-4.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 4\" width=\"664\" height=\"204\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-4.png 664w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-4-300x92.png 300w\" sizes=\"(max-width: 664px) 100vw, 664px\" \/><br \/>\nStep 2: Draw a number line that includes the least and greatest values. Graph points above the number line that represent the five-number summary.<br \/>\nStep 3: Draw a box using the quartiles. Draw a line through the median. Draw whiskers from the box to the least and the greatest values.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16884\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-5.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 5\" width=\"424\" height=\"78\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-5.png 424w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-5-300x55.png 300w\" sizes=\"(max-width: 424px) 100vw, 424px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Try It<\/strong><br \/>\nQuestion 1.<br \/>\nA group of friends spent 1, 0, 2, 3, 4, 3, 6, 1, 0, 1, 2, and 2 hours online last night.Make a box-and-whisker plot for the data.<br \/>\nAnswer:<\/p>\n<p>The figure shows how data are distributed in a box-and-whisker plot.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16885\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-6.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 6\" width=\"623\" height=\"155\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-6.png 623w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-6-300x75.png 300w\" sizes=\"(max-width: 623px) 100vw, 623px\" \/><\/p>\n<p><strong>EXAMPLE 2<\/strong><br \/>\nAnalyzing a Box-and-Whisker Plot<br \/>\nThe box-and-whisker plot shows the body mass index (BMI) of a sixth-grade class.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16886\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-7.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 7\" width=\"658\" height=\"217\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-7.png 658w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-7-300x99.png 300w\" sizes=\"(max-width: 658px) 100vw, 658px\" \/><br \/>\na. What fraction of the students have a BMI of at least 22?<br \/>\nThe right whisker represents students who have a BMI of at least 22.<br \/>\nSo, about \\(\\frac{1}{4}\\) of the students have a BMI of at least 22.<br \/>\nb. Are the data more spread out below the first quartile or above the third quartile? Explain.<br \/>\nThe right whisker is longer than the left whisker.<br \/>\nSo, the data are more spread out above the third quartile than below the first quartile.<br \/>\nc. Find and interpret the interquartile range of the data.<br \/>\ninterquartile range = third quartile \u2212 first quartile<br \/>\n= 22 &#8211; 19 = 3<br \/>\nSo, the middle half of the students\u2019 BMIsvaries by no more than 3.<\/p>\n<p><strong>Try It<\/strong><br \/>\nQuestion 2.<br \/>\nThe box-and-whisker plot shows the heights of the roller coasters at an amusement park.<br \/>\n(a) What fraction of the roller coasters are between 120 feet tall and 220 feet tall?<br \/>\n(b) Are the data more spread out below or above the median? Explain.<br \/>\n(c) Find and interpret the interquartile range of the data.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16887\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-8.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 8\" width=\"437\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-8.png 437w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-8-300x56.png 300w\" sizes=\"(max-width: 437px) 100vw, 437px\" \/><br \/>\nAnswer:<\/p>\n<p>A box-and-whisker plot also shows the shape of a distribution.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16888\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-9.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 9\" width=\"695\" height=\"191\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-9.png 695w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-9-300x82.png 300w\" sizes=\"(max-width: 695px) 100vw, 695px\" \/><\/p>\n<p><strong>EXAMPLE 3<\/strong><br \/>\nIdentifying Shapes of Distributions<br \/>\nThe double box-and-whisker plot represents the life spans of crocodiles and alligators at a zoo. Identify the shape of the distribution of the lifespans of alligators.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16889\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-10.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 10\" width=\"446\" height=\"100\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-10.png 446w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-10-300x67.png 300w\" sizes=\"(max-width: 446px) 100vw, 446px\" \/><br \/>\nFor alligator life spans, the whisker lengths are equal. The median is in the middle of the box. The left side of the box-and-whisker plot is a mirror image of the right side of the box-and-whisker plot.<br \/>\nSo, the distribution is symmetric.<br \/>\nAnswer:<\/p>\n<p><strong>Try It<\/strong><br \/>\nQuestion 3.<br \/>\nIdentify the shape of the distribution of the life spans of crocodiles.<br \/>\nAnswer:<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<br \/>\nQuestion 4.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nExplain how to find the five-number summary of a data set.<br \/>\nAnswer:<\/p>\n<p><strong>MAKING A BOX-AND-WHISKER PLOT<\/strong><br \/>\nMake a box-and-whisker plot for the data. Identify the shape of the distribution.<br \/>\nQuestion 5.<br \/>\nTicket prices (dollars): 39, 42, 40, 47, 38, 39, 44, 55, 44, 58, 45<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nNumber of sit-ups: 20, 20, 23, 25, 25, 26, 27, 29, 30, 30, 32, 34, 37, 38<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nIn a box-and-whisker plot, what fraction of the data is greater than the first quartile?<br \/>\nAnswer:<\/p>\n<p><strong>EXAMPLE 4<\/strong><br \/>\nModeling Real Life<br \/>\nThe double box-and-whisker plot represents the prices of snowboards at two stores.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16890\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-11.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 11\" width=\"671\" height=\"257\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-11.png 671w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-11-300x115.png 300w\" sizes=\"(max-width: 671px) 100vw, 671px\" \/><br \/>\na. Which store\u2019s prices are more spread out? Explain. Both boxes appear to be the same length. So, the interquartile range of each data set is equal. The range of the prices in Store B, however, is greater than the range of the prices in Store A.<br \/>\nSo, the prices in Store B are more spread out.<br \/>\nb. Which store\u2019s prices are generally higher? Explain.<br \/>\nFor Store A,the distribution is symmetric with about one-half of the prices above $300.<br \/>\nFor Store B, the distribution is skewed right with about three-fourths of the prices above $300.<br \/>\nSo, the prices in Store B are generally higher.<br \/>\nAnswer:<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<br \/>\nQuestion 8.<br \/>\nThe tables at the left show the test scores of two sixth-grade achievement tests. The same group of students took both tests. The students took one test in the fall and the other in the spring.<br \/>\na. Analyze each distribution. Then compare and contrast the test results.<br \/>\nb. Which table likely represents the results of which test? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16891\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-12.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 12\" width=\"183\" height=\"178\" \/><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nMake a box-and-whisker plot that represents the heights of the boys in your class. Then make a box-and-whisker plot that represents the heights of the girls in your class. Compare and contrast the distributions.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Box_and_Whisker_Plots_Homework_&amp;_Practice_10.5\"><\/a>Box-and-Whisker Plots Homework &amp; Practice 10.5<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Choose the most appropriate measures to describe the center and the variation.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16892\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-13.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 13\" width=\"241\" height=\"134\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16893\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-14.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 14\" width=\"194\" height=\"150\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Copy and complete the statement using &lt; or &gt;.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16894\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-15.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 15\" width=\"93\" height=\"51\" \/><br \/>\nAnswer: &#8211;\\(\\frac{2}{3}\\) &gt; &#8211;\\(\\frac{3}{4}\\)<\/p>\n<p>Explanation:<br \/>\nCompare fractions to find which fraction is larger and which is smaller.<br \/>\nThe least common denominator (LCD) is 12<br \/>\nRewriting as equivalent fractions with the LCD:<br \/>\n\\(\\frac{2}{3}\\) = \\(\\frac{8}{12}\\)<br \/>\n\\(\\frac{3}{4}\\) = \\(\\frac{9}{12}\\)<br \/>\nNow compare the fractions<br \/>\n&#8211;\\(\\frac{8}{12}\\) &gt;-\\(\\frac{9}{12}\\)<br \/>\nThus we can say that &#8211;\\(\\frac{2}{3}\\) &gt; &#8211;\\(\\frac{3}{4}\\)<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16895\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-16.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 16\" width=\"114\" height=\"53\" \/><br \/>\nAnswer: -2 \\(\\frac{1}{5}\\) &lt; -2 \\(\\frac{1}{6}\\)<\/p>\n<p>Explanation:<br \/>\nCompare fractions to find which fraction is larger and which is smaller.<br \/>\nRewriting these inputs as fractions:<br \/>\n2 \\(\\frac{1}{5}\\) = \\(\\frac{11}{5}\\)<br \/>\n2 \\(\\frac{1}{6}\\) = \\(\\frac{13}{6}\\)<br \/>\nThe LCM is 30<br \/>\nRewriting as equivalent fractions with the LCD<br \/>\n\\(\\frac{11}{5}\\) = \\(\\frac{66}{30}\\)<br \/>\n\\(\\frac{13}{6}\\) = \\(\\frac{65}{30}\\)<br \/>\n&#8211; \\(\\frac{66}{30}\\) &lt; &#8211; \\(\\frac{65}{30}\\)<br \/>\n-2 \\(\\frac{1}{5}\\) &lt; -2 \\(\\frac{1}{6}\\)<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16896\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-17.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 17\" width=\"100\" height=\"37\" \/><br \/>\nAnswer: -5.3 &gt; -5.5<\/p>\n<p>Explanation:<br \/>\nCompare fractions to find which fraction is larger and which is smaller.<br \/>\nThe smallest number with the negative sign will be the greater number<br \/>\nThus -5.3 &gt; -5.5<\/p>\n<p><strong>Factor the expression using the GCF.<\/strong><br \/>\nQuestion 6.<br \/>\n42 + 14<br \/>\nAnswer<\/p>\n<p>Question 7.<br \/>\n12x &#8211; 18<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n28n + 20<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n60g &#8211; 25h<br \/>\nAnswer:<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>COMPARING DATA<\/strong> Compare the data in the box-and-whisker plots. (See Exploration 1, p. 483.)<br \/>\nQuestion 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16897\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-18.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 18\" width=\"213\" height=\"110\" \/><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16898\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-19.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 19\" width=\"212\" height=\"108\" \/><br \/>\nAnswer:<\/p>\n<p><strong>MAKING A BOX-AND-WHISKER PLOT<\/strong><br \/>\nMake a box-and-whisker plot for the data.<br \/>\nQuestion 12.<br \/>\nAges of teachers (in years): 30, 62, 26, 35, 45, 22, 49, 32, 28, 50, 42, 35<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nQuiz scores: 8, 12, 9, 10, 12, 8, 5, 9, 7, 10, 8, 9, 11<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nDonations (in dollars): 10, 30, 5, 15, 50, 25, 5, 20, 15, 35, 10, 30, 20<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nScience test scores: 85, 76, 99, 84, 92, 95, 68, 100, 93, 88, 87, 85<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\nShoe sizes: 12, 8.5, 9, 10, 9, 11, 11.5, 9, 9, 10, 10, 10.5, 8<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nSki lengths (in centimeters): 180, 175, 205, 160, 210, 175, 190, 205, 190, 160, 165, 195<br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend makes a box-and-whisker plot for the data shown. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16899\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-20.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 20\" width=\"286\" height=\"113\" \/><br \/>\n2, 6, 4, 3, 7, 4, 6, 9, 6, 8, 5, 7<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe numbers of days 12 friends went camping during the summer are 6, 2, 0, 10, 3, 6, 6, 4, 12, 0, 6, and 2. Make a box-and-whisker plot for the data. What is the range of the data?<br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\n<strong>ANALYZING A BOX-AND-WHISKER PLOT<\/strong><br \/>\nThe box-and-whisker plot represents the numbers of gallons of water needed to fill different types of dunk tanks offered by a company.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16900\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-21.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 21\" width=\"568\" height=\"194\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-21.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-21-300x102.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><br \/>\na. What fraction of the dunk tanks requires at least 500 gallons of water?<br \/>\nb. Are the data more spread out below the first quartile or above the third quartile? Explain.<br \/>\nc. Find and interpret the interquartile range of the data.<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe box-and-whisker plot represents the heights (in meters) of the tallest buildings in Chicago.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16901\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-22.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 22\" width=\"537\" height=\"282\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-22.png 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-22-300x158.png 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><br \/>\na. What percent of the buildings are no taller than 345 meters?<br \/>\nb. Is there more variability in the heights above 345 meters or below 260.5 meters? Explain.<br \/>\nc. Find and interpret the interquartile range of the data.<br \/>\nAnswer:<\/p>\n<p>Question 22.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nThe numbers of spots on several frogs in a jungle are shown in the dot plot.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16902\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-23.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 23\" width=\"590\" height=\"95\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-23.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-23-300x48.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><br \/>\na. Make a box-and-whisker plot for the data.<br \/>\nb. Compare the dot plot and the box-and-whisker plot. Describe the advantages and disadvantages of each data display.<br \/>\nAnswer:<\/p>\n<p><strong>SHAPES OF BOX-AND-WHISKER PLOTS<\/strong><br \/>\nIdentify the shape of the distribution. Explain.<br \/>\nQuestion 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16903\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-24.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 24\" width=\"213\" height=\"49\" \/><br \/>\nAnswer:<\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-25.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 25\" width=\"157\" height=\"39\" \/><br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16905\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-26.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 26\" width=\"182\" height=\"44\" \/><br \/>\nAnswer:<\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16906\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-27.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 27\" width=\"233\" height=\"36\" \/><br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe double box-and-whisker plot represents the start times of recess for classes at two schools.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16907\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-28.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 28\" width=\"597\" height=\"248\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-28.png 597w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-28-300x125.png 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><br \/>\na. Identify the shape of each distribution.<br \/>\nb. Which school\u2019s start times for recess are more spread out? Explain.<br \/>\nc. You randomly pick one class from each school. Which class is more likely to have recess before lunch? Explain.<br \/>\nAnswer:<\/p>\n<p><strong>MAKING A BOX-AND-WHISKER PLOT<\/strong><br \/>\nMake a box-and-whisker plot for the data.<br \/>\nQuestion 28.<br \/>\nTemperatures (in \u00b0C): 15, 11, 14, 10, 19, 10, 2, 15, 12, 14, 9, 20, 17, 5<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\nChecking account balances (in dollars): 30, 0, 50, 20, 90, \u221215, 40, 100, 45, \u221220, 70, 0<br \/>\nAnswer:<\/p>\n<p>Question 30.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe data set in Exercise 28 has an outlier. Describe how removing the outlier affects the box-and-whisker plot.<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite a data set with 12 values that has a symmetric box-and-whisker plot.<br \/>\nAnswer:<\/p>\n<p>Question 32.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nWhen does a box-and-whisker plot not have one or both whiskers?<br \/>\nAnswer: A simpler formulation is this: no whisker will be visible if the lower quartile is equal to the minimum, or if the upper quartile is equal to the maximum.<\/p>\n<p>Question 33.<br \/>\nSTRUCTURE Draw a histogram that could represent the distribution shown in Exercise 25.<br \/>\nAnswer:<\/p>\n<p>Question 34<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe double box-and-whisker plot represents the goals scored per game by two lacrosse teams during a 16-game season.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16908\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-29.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays 10.5 29\" width=\"596\" height=\"398\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-29.png 596w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-10.5-29-300x200.png 300w\" sizes=\"(max-width: 596px) 100vw, 596px\" \/><br \/>\na. Which team is more consistent? Explain.<br \/>\nb. Team 1 played Team 2 once during the season. Which team do you think won? Explain.<br \/>\nc. Can you determine the number of games in which Team 2 scored 10 goals or less? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<strong>CHOOSE TOOLS<\/strong><br \/>\nA market research company wants to summarize the variability of the SAT scores of graduating seniors in the United States. Should the company use a stem-and-leaf plot, a histogram, or a box-and-whisker plot? Explain.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Data_Displays_Connecting_Concepts\"><\/a>Data Displays Connecting Concepts<\/h3>\n<p>Using the Problem-Solving Plan<br \/>\n1. The locations of pitches in an at-bat are shown in the coordinate plane, where the coordinates are measured in inches. Describe the location of a typical pitch in the at-bat.<br \/>\nUnderstand the problem<br \/>\nYou know the locations of the pitches. You are asked to find the location of a typical pitch in the at-bat.<\/p>\n<p>Make a plan<br \/>\nFirst, use the coordinates of the pitches to create two data sets, one for the x-coordinates of the pitches and one for the y-coordinates of the pitches. Next, make a box-and-whisker plot for each data set. Then use the most appropriate measure of center for each data set to find the location of a typical pitch.<\/p>\n<p>Solve and check<br \/>\nUse the plan to solve the problem. Then check your solution.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16909\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-cc-1.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays cc 1\" width=\"321\" height=\"486\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-cc-1.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-cc-1-198x300.png 198w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><\/p>\n<p>2. A set of 20 data values is described below. Sketch a histogram that could represent the data set. Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16910\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-cc-2.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays cc 2\" width=\"164\" height=\"186\" \/><br \/>\n\u2022 least value: 10<br \/>\n\u2022 first quartile: 25<br \/>\n\u2022 mean: 29<br \/>\n\u2022 third quartile: 34<br \/>\n\u2022 greatest value: 48<br \/>\n\u2022 MAD: 7<\/p>\n<p>3. The chart shows the dimensions (in inches) of several flat-rate shipping boxes. Each box is in the shape of a rectangular prism. Describe the distribution of the volumes of the boxes. Then find the most appropriate measures to describe the center and the variation of the volumes.<\/p>\n<p><strong>Performance Task<\/strong><br \/>\nClassifying Dog Breeds by Size<br \/>\nAt the beginning of this chapter, you watched a STEAM Video called \u201cChoosing a Dog.\u201d You are now ready to complete the performance task related to this video, available at BigIdeasMath.com. Be sure to use the problem-solving plan as you work through the performance task.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16911\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-cc-3.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays cc 3\" width=\"345\" height=\"184\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-cc-3.png 345w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-cc-3-300x160.png 300w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><\/p>\n<h3><a id=\"Data_Displays_Chapter_Review\"><\/a>Data Displays Chapter Review<\/h3>\n<p><strong>Review Vocabulary<\/strong><br \/>\nWrite the definition and give an example of each vocabulary term.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16912\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-cr-1.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays cr 1\" width=\"588\" height=\"69\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-cr-1.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-cr-1-300x35.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p><strong>Graphic Organizers<\/strong><br \/>\nYou can use an Information Frame to help you organize and remember concepts. Here is an example of an Information Frame for the vocabulary term histogram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16913\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-cr-2.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays cr 2\" width=\"504\" height=\"649\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-cr-2.png 504w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-cr-2-233x300.png 233w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><br \/>\nChoose and complete a graphic organizer to help you study the concept.<br \/>\n1. stem-and-leaf plot<br \/>\n2. frequency table<br \/>\n3. shapes of distributions<br \/>\n4. box-and-whisker plot<br \/>\nAnswer:<\/p>\n<p><strong>Chapter Self-Assessment<\/strong><br \/>\nAs you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16914\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-cr-3.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays cr 3\" width=\"584\" height=\"72\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-cr-3.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-cr-3-300x37.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p><strong>10.1 Stem-and-Leaf Plots<\/strong><br \/>\n<strong>Learning Target: Display and interpret data in stem-and-leaf plots.<\/strong><\/p>\n<p>Make a stem-and-leaf plot of the data.<br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16915\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-crr-1.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays crr 1\" width=\"201\" height=\"130\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34119\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-img_16-300x212.jpg\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays img_16\" width=\"300\" height=\"212\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-img_16-300x212.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-img_16.jpg 334w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16916\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-crr-2.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays crr 2\" width=\"202\" height=\"123\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34120\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-img_17-300x212.jpg\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays img_17\" width=\"300\" height=\"212\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-img_17-300x212.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-img_17.jpg 334w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 3.<br \/>\nThe stem-and-leaf plot shows the weights (in pounds) of yellowfin tuna caught during a fishing contest.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16917\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-crr-3.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays crr 3\" width=\"215\" height=\"140\" \/><br \/>\na. How many tuna weigh less than 90 pounds?<br \/>\nb. Find the mean, median, mode, range, and interquartile range of the data.<br \/>\nc. How are the data distributed?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nThe stem-and-leaf plot shows the body mass index (BMI) for adults at a recreation center. Use the data to answer the question, \u201cWhat is the typical BMI for an adult at the recreation center?\u201d Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16918\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-crr-4.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays crr 4\" width=\"199\" height=\"115\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nWrite a statistical question that can be answered using the stem-and-leaf plot.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16919\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-crr-5.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays crr 5\" width=\"213\" height=\"153\" \/><br \/>\nAnswer:<\/p>\n<p><strong>10.2 Histograms (pp. 463-470)<\/strong><br \/>\n<strong>Learning Target: Display and interpret data in histograms.<\/strong><\/p>\n<p>Display the data in a histogram.<br \/>\nQuestion 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16920\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-crr-6.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays crr 6\" width=\"227\" height=\"152\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34122\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-img_18-300x212.jpg\" alt=\"\" width=\"300\" height=\"212\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-img_18-300x212.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-img_18.jpg 334w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16921\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-crr-7.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays crr 7\" width=\"214\" height=\"153\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34123\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-img_19-300x212.jpg\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays img_19\" width=\"300\" height=\"212\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-img_19-300x212.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-10-Data-Displays-img_19.jpg 334w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 8.<br \/>\nThe histogram shows the number of crafts each member of a craft club made for a fundraiser.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16922\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-crr-8.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays crr 8\" width=\"217\" height=\"169\" \/><br \/>\na. Which interval contains the most data values?<br \/>\nb. Frequency How many members made at least 6 crafts?<br \/>\nc. Can you use the histogram to determine the total number of crafts made? Explain.<br \/>\nAnswer:<\/p>\n<p><strong>10.3 Shapes of Distributions (pp. 471\u2013476)<\/strong><br \/>\n<strong>Learning Target: Describe and compare shapes of distributions.<\/strong><\/p>\n<p>Question 9.<br \/>\nDescribe the shape of the distribution.<br \/>\nAnswer: The shape of a distribution is described by its number of peaks and by its possession of symmetry, its tendency to skew, or its uniformity.<\/p>\n<p>Question 10.<br \/>\nThe frequency table shows the math test scores for the same class of students as Exercise 9. Display the data in a histogram. Which test has higher scores?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16923\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-crr-10.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays crr 10\" width=\"536\" height=\"180\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-crr-10.png 536w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-crr-10-300x101.png 300w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nThe table shows the numbers of neutrons for several elements in the nonmetal group of the periodic table. Make a histogram of the data starting with the interval 0\u20139. Describe the shape of the distribution.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16924\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-crr-11.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays crr 11\" width=\"160\" height=\"91\" \/><br \/>\nAnswer:<\/p>\n<p><strong>10.4 Choosing Appropriate Measures (pp. 477\u2013482)<\/strong><br \/>\nLearning Target: Use the shape of the distribution of a data set to determine which measures of center and variation best describe the data.<\/p>\n<p>Choose the most appropriate measures to describe the center and the variation. Students\u2019 Heights<br \/>\nQuestion 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16925\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-crr-12.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays crr 12\" width=\"226\" height=\"158\" \/><br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16926\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-crr-13.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays crr 13\" width=\"210\" height=\"144\" \/><br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nDescribe the center and the variation of the data set in Exercise 13.<br \/>\nAnswer:<\/p>\n<p><strong>10.5 Box-and-Whisker Plots (pp. 483\u2013490)<\/strong><br \/>\n<strong>Learning Target: Display and interpret data in box-and-whisker plots.<\/strong><\/p>\n<p>Make a box-and-whisker plot for the data.<br \/>\nQuestion 15.<br \/>\nAges of volunteers at a hospital:<br \/>\n14, 17, 20, 16, 17, 14, 21, 18<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\nMasses (in kilograms) of lions:<br \/>\n120, 200, 180, 150, 200, 200, 230, 160<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nThe box-and-whisker plot represents the lengths (in minutes) of movies being shown at a theater.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16927\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-crr-17.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays crr 17\" width=\"448\" height=\"74\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-crr-17.png 448w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-crr-17-300x50.png 300w\" sizes=\"(max-width: 448px) 100vw, 448px\" \/><br \/>\na. What percent of the movies are no longer than 120 minutes?<br \/>\nb. Is there more variability in the movie lengths longer than 130 minutes or shorter than 110 minutes? Explain.<br \/>\nc. Find and interpret the interquartile range of the data.<br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\nThe double box-and-whisker plot represents the heights of students in two math classes.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16928\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-6th-Grade-Chapter-10-Data-Displays-crr-18.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 10 Data Displays crr 18\" width=\"269\" height=\"101\" \/><br \/>\na. Identify the shape of each distribution.Height(cm)<br \/>\nb.Which class has heights that are more spread out? Explain.<br \/>\nc.You randomly pick one student from each class. Which student is more likely to be taller than 170 centimeters? Explain.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Data_Displays_Practice_Test\"><\/a>Data Displays Practice Test<\/h3>\n<p>Make a stem-and-leaf plot of the data.<br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16929\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-pt-1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays pt 1\" width=\"184\" height=\"116\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-29630\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-img_8.jpg\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays img_8\" width=\"236\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-img_8.jpg 236w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-img_8-150x150.jpg 150w\" sizes=\"(max-width: 236px) 100vw, 236px\" \/><\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16930\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-pt-2.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays pt 2\" width=\"222\" height=\"117\" \/><br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-29634\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-img_9.jpg\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays img_9\" width=\"236\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-img_9.jpg 236w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-img_9-150x150.jpg 150w\" sizes=\"(max-width: 236px) 100vw, 236px\" \/><\/p>\n<p>Question 3.<br \/>\nFind the mean, median, mode, range, and interquartile range of the data.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16931\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-pt-3.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays pt 3\" width=\"223\" height=\"148\" \/><br \/>\nAnswer:<br \/>\nGiven data 35, 38, 40, 41, 48, 50, 54, 54, 54, 55, 59, 60<br \/>\nMean:<br \/>\nThe mean refers to an intermediate value between a discrete set of numbers, namely, the sum of all values in the data set, divided by the total number of values.<br \/>\nx\u0304 = (35+38+40+41+48+50+54+54+54+55+59+60)\/12<br \/>\nx\u0304 = 49<br \/>\nThus mean of the given data is 49.<br \/>\nMedian:<br \/>\nGiven data 35, 38, 40, 41, 48, 50, 54, 54, 54, 55, 59, 60<br \/>\nIn the case where the total number of values in a data sample is odd, the median is simply the number in the middle of the list of all values. When the data sample contains an even number of values, the median is the mean of the two middle values.<br \/>\nMedian = (50+54)\/2 = 104\/2 = 52<br \/>\nThus the median of the given data is 52.<br \/>\nMode:<br \/>\nThe mode is the value in a data set that has the highest number of recurrences.<br \/>\n35, 38, 40, 41, 48, 50, 54, 54, 54, 55, 59, 60<br \/>\nMode = 54 (repeated 3 times)<\/p>\n<p>Question 4.<br \/>\nDisplay the data in a histogram. How many people watched less than 20 hours of television per week?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16932\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-pt-4.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays pt 4\" width=\"229\" height=\"151\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-29742\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Chapter-10-Data-Displays-Answer-Key-img_10-300x253.jpg\" alt=\"BIM Grade 6 Chapter 10 Data Displays Answer Key img_10\" width=\"300\" height=\"253\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Chapter-10-Data-Displays-Answer-Key-img_10-300x253.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-6-Chapter-10-Data-Displays-Answer-Key-img_10.jpg 327w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nBy seeing the above histogram we can find the number of people who watched less than 20 hours of television per week.<br \/>\n14 + 16 = 30<br \/>\nTherefore 30 people watched less than 20 hours per week.<\/p>\n<p>Question 5.<br \/>\nThe dot plot shows the numbers of glasses of water Water Consumed that the students in a class drink in one day.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16933\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-pt-5.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays pt 5\" width=\"266\" height=\"123\" \/><br \/>\na. Describe the shape of the distribution.<br \/>\nb. Choose the most appropriate measures to describe the center and the variation. Find the measures you chose.<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nMake a box-and-whisker plot for the lengths (in inches) of fish in a pond: 12, 13, 7, 8, 14, 6, 13, 10.<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nThe double box-and-whisker plot compares the battery lives (in hours) of two brands of cell phones.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16934\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-pt-7.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 10 Data Displays pt 7\" width=\"570\" height=\"337\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-pt-7.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-6-Chapter-10-Data-Displays-pt-7-300x177.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><br \/>\na. What is the range of the upper 75% of battery life for each brand of cell phone?<br \/>\nb. Which brand of cell phone typically has a longer battery life? Explain.<br \/>\nc. In the box-and-whisker plot, there are 190 cell phones of Brand A that have at most 10.5 hours of battery life. About how many cell phones are represented in the box-and-whisker plot for Brand A?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Data_Displays_Cumulative_Practice\"><\/a>Data Displays Cumulative Practice<\/h3>\n<p>Question 1.<br \/>\nResearch scientists are measuring the numbers of days lettuce seeds take to germinate. In a study, 500 seeds were planted. Of these,473 seeds germinated. The box-and-whisker plot summarizes the numbers of days it took the seeds to germinate. What can you conclude from the box-and-whisker plot?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16935\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-cp-1.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays cp 1\" width=\"635\" height=\"365\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-cp-1.png 635w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-cp-1-300x172.png 300w\" sizes=\"(max-width: 635px) 100vw, 635px\" \/><br \/>\nA. The median number of days for the seeds to germinate is 12.<br \/>\nB. 50% of the seeds took more than 8 days to germinate.<br \/>\nC. 50% of the seeds took less than 5 days to germinate.<br \/>\nD. The median number of days for the seeds to germinate was 6.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nFind the interquartile range of the data.<br \/>\n15 7 5 8 9 20 12 7 11 7 15<br \/>\nF. 8<br \/>\nG. 11<br \/>\nH. 12<br \/>\nI. 20<br \/>\nAnswer: 8<\/p>\n<p>Question 3.<br \/>\nThere are seven different integers in a set. When they are listed from least to greatest, the middle integer is \u22121. Which statement below must be true?<br \/>\nA. There are three negative integers in the set.<br \/>\nB. There are three positive integers in the set.<br \/>\nC. There are four negative integers in the set.<br \/>\nD. The integer in the set after \u22121 is positive.<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nWhat is the mean number of seats?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16936\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-cp-4.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays cp 4\" width=\"238\" height=\"166\" \/><br \/>\nF. 2.4 seats<br \/>\nG. 5 seats<br \/>\nH. 6.5 seats<br \/>\nI. 7 seats5.<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nOn Wednesday, a town received 17 millimeters of rain. This was x millimeters more rain than the town received on Tuesday. Which expression represents the amount of rain, in millimeters, the town received on Tuesday?<br \/>\nA. 17x<br \/>\nB. 17 &#8211; x-c<br \/>\nC. x + 17<br \/>\nD. x &#8211; 17<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nOne of the leaves is missing in the stem-and-leaf plot.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16937\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-cp-6.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays cp 6\" width=\"323\" height=\"147\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-cp-6.png 323w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-cp-6-300x137.png 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><br \/>\nThe median of the data set represented by the stem-and-leaf plot is 38. What is the value of the missing leaf?<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nWhich property is demonstrated by the equation?<br \/>\n723 + (y + 277) = 723 + (277 + y)<br \/>\nF. Associative Property of Addition<br \/>\nG. Commutative Property of Addition<br \/>\nH. Distributive Property<br \/>\nI. Addition Property of Zero<br \/>\nAnswer: Associative Property of Addition<\/p>\n<p>Explanation:<br \/>\nAssociative property of addition: Changing the grouping of addends does not change the sum<br \/>\nThus the correct answer is option F.<\/p>\n<p>Question 8.<br \/>\nA student took five tests and had a mean score of 92. Her scores on the first 4 tests were 90, 96, 86, and 92. What was her score on the fifth test?<br \/>\nA. 92<br \/>\nB. 93<br \/>\nC. 96<br \/>\nD. 98<br \/>\nAnswer: 86<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nA student took five tests and had a mean score of 92.<br \/>\nHer scores on the first 4 tests were 90, 96, 86, and 92.<br \/>\n(90+96+86+92+s)\/5=90<br \/>\n(364+s)\/5=90<br \/>\n364+s=450<br \/>\ns=86<br \/>\nSo she scored an 86 on the fifth test.<\/p>\n<p>Question 9.<br \/>\nAt the end of the school year, your teacher counted the number of absences for each student. The results are shown in the histogram. How many students had fewer than 10 absences?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16938\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-cp-9.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays cp 9\" width=\"350\" height=\"235\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-cp-9.png 350w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-cp-9-300x201.png 300w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nThe ages of the 16 members of a camera club are listed below.<br \/>\n40, 22, 24, 58, 30, 31, 37, 25, 62, 40, 39, 37, 28, 28, 51, 44<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16939\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-cp-10.1.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays cp 10.1\" width=\"74\" height=\"80\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16940\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-cp-10.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 10 Data Displays cp 10\" width=\"394\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-cp-10.png 394w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-6-Chapter-10-Data-Displays-cp-10-300x48.png 300w\" sizes=\"(max-width: 394px) 100vw, 394px\" \/><br \/>\nPart A Order the ages from youngest to oldest.<br \/>\nPart B Find the median of the ages.<br \/>\nPart C Make a box-and-whisker plot for the ages.<br \/>\nAnswer:<\/p>\n<p><i>Final Words:<\/i><\/p>\n<p>You have seen Big Ideas Math Answer Key Grade 6 Chapter 10 Data Displays concept in detail. Hope you are satisfied with the information provided. If you still have any doubts, then you can approach us by the below given comment section. Make use of Big Ideas Math Answers Grade 6 Chapter 10 Data Displays Pdf and overcome all your difficulties. Make sure you stay tuned to site to get the trending and instant updates on all Big Ideas Math Answers Grade 6 Chapters. We wish all the candidates all the very best for the preparation.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Big Ideas Math Answers Grade 6 Chapter 10 Data Displays: Free Download Big Ideas Math Answers Grade 6 Chapter 10 Data Displays Pdf here. Get step by step solution to all the concepts of Stem-and-Leaf Plots, Histograms, Shapes of Distributions, Choosing Appropriate Measures, and so on. 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