{"id":24100,"date":"2022-04-07T09:25:16","date_gmt":"2022-04-07T03:55:16","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=24100"},"modified":"2022-04-07T11:14:31","modified_gmt":"2022-04-07T05:44:31","slug":"big-ideas-math-answers-grade-6-chapter-9","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-6-chapter-9\/","title":{"rendered":"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures"},"content":{"rendered":"<p>Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures Pdf is here. To help all the candidates, we took the help of various experts and professionals and prepared <a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-6\/\">Big Ideas Math Answers Grade 6 <\/a>in pdf format. The pdf format will help you to prepare at home or tuitions as it is available in offline mode. You can get the various chapters involved in Statistical Measures concepts.<\/p>\n<p><strong><em>Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures pdf<\/em><\/strong> is available for free, so you can start practicing all the problems to score maximum marks. Scroll down to the below sections to get the various concepts like Mean, Mass of Center, Measures of Variations, Mean Absolute Deviation, etc.<\/p>\n<h2>Big Ideas Math Book 6th Grade Answer Key Chapter 9 Statistical Measures<\/h2>\n<p>Follow all the concepts of statistical measures which are available in Big Ideas Math Grade 6 Solution Key Chapter 9. This material will help you as a guide for your preparation. If you are looking for all the concepts of statistical measures in one place, then <strong>BIM 6th Grade Chapter 9 Statistical Measures pdf<\/strong> is the best solution. Don&#8217;t waste your time in search of a topic-wise pdf, instead download this whole pdf once and start your preparation.<\/p>\n<p>You can find various level problems here, i.e., easy, tough, and medium level which helps you to analyze your level of preparation and also to overcome your difficulties. Scoring good marks in the exam is the main aim for all the candidates, hence you have to use Big Ideas Math Book 6th Grade Answer Key Chapter 9 Statistical Measures book as a reference.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<ul>\n<li><a href=\"#Statistical_Measures_STEAM_Video\/Performance_Task\">Statistical Measures STEAM Video\/Performance Task<\/a><\/li>\n<li><a href=\"#Statistical_Measures_Getting_Ready_for_Chapter_9\">Statistical Measures Getting Ready for Chapter 9<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 1 Introduction to Statistics<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.1_Introduction_to_Statistics\">Lesson 9.1 Introduction to Statistics<\/a><\/li>\n<li><a href=\"#Introduction_to_Statistics_Homework_&amp;_Practice_9.1\">Introduction to Statistics Homework &amp; Practice 9.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Mean<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.2_Mean\">Lesson 9.2 Mean<\/a><\/li>\n<li><a href=\"#Mean_Homework_&amp;_Practice_9.2\">Mean Homework &amp; Practice 9.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Measures of Center<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.3_Measures_of_Center\">Lesson 9.3 Measures of Center<\/a><\/li>\n<li><a href=\"#Measures_of_Center_Homework_&amp;_Practice_9.3\">Measures of Center Homework &amp; Practice 9.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Measures of Variation<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.4_Measures_of_Variation\">Lesson 9.4 Measures of Variation<\/a><\/li>\n<li><a href=\"#Measures_of_Variation_Homework_&amp;_Practice_9.4\">Measures of Variation Homework &amp; Practice 9.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Mean Absolute Deviation<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.5_Mean_Absolute_Deviation\">Lesson 9.5 Mean Absolute Deviation<\/a><\/li>\n<li><a href=\"#Mean_Absolute_Deviation_Homework_&amp;_Practice_9.5\">Mean Absolute Deviation Homework &amp; Practice 9.5<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 9: Statistical Measures<\/strong><\/p>\n<ul>\n<li><a href=\"#Statistical_Measures_Connecting_Concepts\">Statistical Measures Connecting Concepts<\/a><\/li>\n<li><a href=\"#Statistical_Measures_Chapter_Review\">Statistical Measures Chapter Review<\/a><\/li>\n<li><a href=\"#Statistical_Measures_Practice_Test\">Statistical Measures Practice Test<\/a><\/li>\n<li><a href=\"#Statistical_Measures_Cumulative_Practice\">Statistical Measures Cumulative Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Statistical_Measures_STEAM_Video\/Performance_Task\"><\/a>Statistical Measures STEAM Video\/Performance Task<\/h3>\n<p><strong>STEAM Video<\/strong><br \/>\nDaylight in the Big City<br \/>\nAverages can be used to compare different sets of data. How can you use averages to compare the amounts of day light in different cities? Can you think of any other real-life situations where averages are useful?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24102\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 1\" width=\"177\" height=\"344\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-1.png 177w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-1-154x300.png 154w\" sizes=\"(max-width: 177px) 100vw, 177px\" \/><br \/>\nWatch the STEAM Video \u201cDaylight in the Big City.\u201d Then answer the following questions.<br \/>\n1. Why do different cities have different amounts of daylight throughout the year?<\/p>\n<p>Answer:<br \/>\nOur amount of daylight hours depends on our latitude and how Earth orbits the sun. This causes a seasonal variation in the intensity of sunlight reaching the surface and the number of hours of daylight. The variation in intensity results because the angle at which the sun&#8217;s rays hit the Earth changes with the time of year.<\/p>\n<p>2. Robert\u2019s table includes the difference of the greatest amount of daylight and the least amount of daylight in Lagos, Nigeria, and in Moscow, Russia.<br \/>\nLagos: 44 minutes<br \/>\nMoscow:633 minutes<br \/>\nUse these values to make a prediction about the difference between the greatest amount of daylight and the least amount of daylight in a city in Alaska.<\/p>\n<p>Answer:<br \/>\nThe least daylight in Alaska is 1092 minutes in Juneau<br \/>\nThe greatest daylight in Alaska is 1320 minutes in Fairbanks<\/p>\n<p><strong>Performance Task<\/strong><br \/>\nWhich Measure of Center Is Best: Mean, Median, or Mode?<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 the greatest and least amounts of daylight in the 15 cities in the United States with the greatest populations.<br \/>\ns<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24104\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-3.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 3\" width=\"321\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-3.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-3-300x96.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\nYou will determine which measure of center best represents the data. Why might someone be interested in the amounts of daylight throughout the year in a city?<\/p>\n<h3><a id=\"Statistical_Measures_Getting_Ready_for_Chapter_9\"><\/a>Statistical Measures Getting Ready for Chapter 9<\/h3>\n<p><strong>Chapter Exploration<\/strong><br \/>\nWork with a partner. Write the number of letters in each of your first names on the board.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24105\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-4.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 4\" width=\"278\" height=\"205\" \/><br \/>\n1. Write all of the numbers on a piece of paper. The collection of numbers is called data.<br \/>\n2. Talk with your partner about how you can organize the data. What conclusions can you make about the numbers of letters in the first names of the students in your class?<br \/>\n3. Draw a grid like the one shown below. Then use the grid to draw a graph of the data.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24106\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-5.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 5\" width=\"179\" height=\"151\" \/><\/p>\n<p>Answer:<br \/>\n3,6,9,5,6,7,6,5,5,8,6,8,5,6,4,4,7,6,3,5,6,5,5<\/p>\n<p>4. THE CENTER OF THE DATA Use the graph of the data in Exercise 3 to answer the following.<br \/>\na. Is there one number that occurs more than any of the other numbers? If so, write a sentence that interprets this number in the context of your class.<br \/>\nb. Complete the sentence, \u201cIn my class, the average number of letters in a student\u2019s first name is __________.\u201d Justify your reasoning.<br \/>\nc. Organize your data using a different type of graph. Describe the advantages or disadvantages of this graph.<\/p>\n<p>Answer:<br \/>\na. Yes, 6, 5, 8 are more than other numbers given in the data.<br \/>\nb. \u201cIn my class, the average number of letters in a student\u2019s first name is 5 and 6.<\/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 \/>\nstatistical question<br \/>\nmeasure of center<br \/>\nmeasure of variation<br \/>\nmean<br \/>\nmedian<br \/>\nrange<\/p>\n<h3><a id=\"Lesson_9.1_Introduction_to_Statistics\"><\/a>Lesson 9.1 Introduction to Statistics<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Using Data to Answer a Question<br \/>\nWork with a partner.<br \/>\na. Use your pulse to find your heart rate in beats per minute.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24107\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 1\" width=\"400\" height=\"154\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-1.png 400w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-1-300x116.png 300w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><br \/>\nb. Collect the recorded heart rates of the students in your class, including yourself. How spread out are the data? Use a diagram to justify your answer.<br \/>\nc. REASONING How would you answer the following question by using only one value? Explain your reasoning.<br \/>\n\u201cWhat is the heart rate of a sixth-grade student?\u201d<br \/>\nAnswer: Your pulse\u00a0is\u00a0measured by counting the number of times your heart\u00a0beats\u00a0in one\u00a0minute. For example, if your heart contracts 72 times in one\u00a0minute, your pulse would be 72\u00a0beats per minute\u00a0(BPM).<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Identifying Types of Questions<br \/>\nWork with a partner.<br \/>\na. Answer each question on your own. Then compare your answers with your partner\u2019s answers. For which questions should your answers be the same? For which questions might your answers be different?<br \/>\n1. How many states are in the United States?<br \/>\nAnswer: There are 50 states in the United States.<\/p>\n<p>2. How much does a movie ticket cost? Math Practice<br \/>\nAnswer: $9.16<br \/>\n3. What color fur do bears have? Build Arguments How can comparing your answers help you support your conjecture?<br \/>\nAnswer: The color white becomes visible to our eyes when an object reflects back all.<\/p>\n<p>4. How tall is your math teacher?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24108\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-2.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 2\" width=\"136\" height=\"138\" \/><br \/>\nb. CONJECTURE<br \/>\nSome of the questions in part(a) are considered statistical questions. Which ones are they? Explain.<br \/>\nAnswer: 5.10 inches<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-24109\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-3.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 3\" width=\"185\" height=\"173\" \/><\/p>\n<p>Statistics is the science of collecting, organizing, analyzing, and interpreting data. A statistical question is one for which you do not expect to get a single answer. Instead, you expect a variety of answers, and you are interested in the distribution and tendency of those answers.<\/p>\n<p><strong>Try It<\/strong><br \/>\nDetermine whether the question is a statistical question. Explain.<br \/>\nQuestion 1.<br \/>\nWhat types of cell phones do students have in your class?<br \/>\nAnswer:<br \/>\nSmartphones, Cell phones\u00a0give\u00a0students\u00a0access to tools and apps that can help them complete and stay on top of their\u00a0class\u00a0work. These tools can also teach\u00a0students\u00a0to develop better study habits, like time management and organization skills.<\/p>\n<p>Question 2.<br \/>\nHow many desks are in your classroom?<br \/>\nAnswer: 25<\/p>\n<p>Question 3.<br \/>\nHow much do virtual-reality headsets cost?<br \/>\nAnswer: $499<\/p>\n<p>Question 4.<br \/>\nHow many minutes are in your lunch period?<br \/>\nAnswer: 45 minutes<\/p>\n<p>A dot plot uses a number line to show the number of times each value in a data set occurs. Dot plots show the spread and the distribution of a data set.<\/p>\n<p>Question 5.<br \/>\nRepeat parts (a)\u2013(c)using the dot plot below that shows the times of students in a 100-meter race.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24113\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-7.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 7\" width=\"358\" height=\"92\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-7.png 358w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-7-300x77.png 300w\" sizes=\"(max-width: 358px) 100vw, 358px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p style=\"text-align: left;\">Solve each exercise. Then rate your understanding of the success criteria in your journal.<br \/>\nQuestion 6.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhat is a statistical question? Give an example and a non-example.<br \/>\nAnswer:<br \/>\nEg for statistical question: a. How much do bags of pretzels cost at the grocery store?<br \/>\nBecause you can anticipate that the prices will vary, it is a statistical question. table at the right may represent the prices of several bags of pretzels at a grocery store.<br \/>\nEg for non-statistical question: b.\u00a0How many days does your school have o\ufb00 for spring break this year?<br \/>\nAnswer: Because there is only one answer, it is not a statistical question.<\/p>\n<p>Question 7.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite and answer a statistical question using the dot plot. Then find and interpret the number of data values.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24114\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-8.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 8\" width=\"383\" height=\"82\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-8.png 383w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-8-300x64.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><br \/>\nAnswer: There are 16 data values on the dot plot.<\/p>\n<p>Question 8.<br \/>\nYou record the amount of snowfall each day for several days. Then you create the dot plot.<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-24117\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-11.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 11\" width=\"190\" height=\"67\" \/><br \/>\na. Find and interpret the number of data values on the dot plot.<br \/>\nAnswer: There are 13 data values on the dot plot.<\/p>\n<p>b. How can you collect these data? What are the units?<br \/>\nAnswer: We can collect the data by using the dots given in the above figure.<br \/>\nc. Write a statistical question that you can answer using the dot plot. Then answer the question.<br \/>\nAnswer: dot plots are best used to show a distribution of data.<\/p>\n<p>Question 9.<br \/>\nYou conduct a survey to answer, \u201cHow many hours does a typical sixth-grade student spend exercising during a week?\u201d Use the data in the table to answer the question.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24118\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-12.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 12\" width=\"174\" height=\"121\" \/><br \/>\nAnswer:<br \/>\nGiven the data<br \/>\n5, 1, 5, 3, 5, 4, 5, 2, 5, 4, 3, 4, 6, 5, 6<br \/>\nThe typical sixth-grade student spend exercising during a week is 6 hours.<\/p>\n<h3><a id=\"Introduction_to_Statistics_Homework_&amp;_Practice_9.1\"><\/a>Introduction to Statistics Homework &amp; Practice 9.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Solve the inequality. Graph the solution.<\/strong><br \/>\nQuestion 1.<br \/>\nx &#8211; 16 &gt; 8<br \/>\nAnswer: x&gt;3.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-medium wp-image-56247\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-9-statistical-measures-img_1-300x56.jpg\" alt=\"big ideas math answers grade 6 chapter 9 statistical measures img_1\" width=\"300\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-9-statistical-measures-img_1-300x56.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-9-statistical-measures-img_1.jpg 519w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 2.<br \/>\np + 6 \u2264 8<br \/>\nAnswer:\u00a0 \u00a0p \u2264 2<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-medium wp-image-56249\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-9-statistical-measures-img_2-300x56.jpg\" alt=\"big ideas math answers grade 6 chapter 9 statistical measures img_2\" width=\"300\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-9-statistical-measures-img_2-300x56.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-9-statistical-measures-img_2.jpg 519w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 3.<br \/>\n54 &gt; 6k<br \/>\nAnswer: 9&gt;k<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-medium wp-image-56250\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-9-statistical-measures-img_3-300x56.jpg\" alt=\"big ideas math answers grade 6 chapter 9 statistical measures img_3\" width=\"300\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-9-statistical-measures-img_3-300x56.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-9-statistical-measures-img_3.jpg 519w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 4.<br \/>\n\\(\\frac{m}{12}\\) \u2265 3<br \/>\nAnswer: m \u2264 36<\/p>\n<p><strong>Tell whether the ordered pair is a solution of the equation.<\/strong><br \/>\nQuestion 5.<br \/>\ny = 4x; (2, 8)<br \/>\nAnswer: The given ordered pair is a solution of the equation.<br \/>\nGiven : y = 4x;(2,8)<br \/>\ny=8;x=2<br \/>\n8=4 \u00d7 2<br \/>\n8=8 (satisfied)<\/p>\n<p>Question 6.<br \/>\ny = 3x + 5; (3, 15)<br \/>\nAnswer: Given order pair is not an absolute solution of ordered pair<br \/>\nGiven: y = 3x + 5; (3, 15)<br \/>\ny=15;x=3<br \/>\n15=3(3)+5<br \/>\n15=9+5<br \/>\n15=14 (not satisfied)<\/p>\n<p>Question 7.<br \/>\ny = 6x &#8211; 15; (4, 9)<br \/>\nAnswer:<br \/>\nThe given ordered pair is a solution of the equation.<br \/>\nGiven: y = 6x &#8211; 15; (4, 9)<br \/>\n9=6(4)-15<br \/>\n9=24-15<br \/>\n9=9<\/p>\n<p>Question 8.<br \/>\nA point is reflected in the x-axis. The reflected point is (4, \u22123). What is the original point?<br \/>\nA. (-3, 4)<br \/>\nB. (-4, 3)<br \/>\nC. (-4, -3)<br \/>\nD. (4, 3)<br \/>\nAnswer: B,(-4,3)<\/p>\n<p><strong>Order the numbers from least to greatest.<\/strong><br \/>\nQuestion 9.<br \/>\n24%, \\(\\frac{1}{4}\\) , 0.2, \\(\\frac{7}{20}\\) , 0.32<br \/>\nAnswer:0.24,0.25,0.2.0.35,0.32<br \/>\n0.2,0.24,0.32,0.35<\/p>\n<p>Question 10.<br \/>\n\\(\\frac{7}{8}\\), 85%, 0.88, \\(\\frac{3}{4}\\) , 78%<br \/>\nAnswer:0.875,0.78,0.88,0.75,0.78<br \/>\n0.75,0.78,0.85,0.875,0.88<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p>IDENTIFYING TYPES OF QUESTIONS Answer the question. Tell whether your answer should be the same as your classmates\u2019. (See Exploration 2, p. 413.)<br \/>\nQuestion 11.<br \/>\nHow many inches are in 1 foot?<br \/>\nAnswer: 12 inches<\/p>\n<p>Question 12.<br \/>\nHow many pets do you have?<br \/>\nAnswer: none<\/p>\n<p>Question 13.<br \/>\nOn what day of the month were you born?<br \/>\nAnswer: 27th April<\/p>\n<p>Question 14.<br \/>\nHow many senators are in Congress?<br \/>\nAnswer: The Senate is composed of 100 Senators, 2 for each state. Until the ratification of the 17th Amendment in 1913, Senators were chosen by state legislatures, not by popular vote. Since then, they have been elected to six-year terms by the people of each state.<\/p>\n<p><strong>IDENTIFYING STATISTICAL QUESTIONS<\/strong><br \/>\nDetermine whether the question is a statistical question. Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24119\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-13.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 13\" width=\"210\" height=\"352\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-13.png 210w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-13-179x300.png 179w\" sizes=\"(max-width: 210px) 100vw, 210px\" \/><br \/>\nQuestion 15.<br \/>\nWhat are the eye colors of sixth-grade students?<br \/>\nAnswer: brown<\/p>\n<p>Question 16.<br \/>\nAt what temperature (in degrees Fahrenheit) does water freeze?<br \/>\nAnswer: 32 degrees Fahrenheit<\/p>\n<p>Question 17.<br \/>\nHow many pages are in the favorite books of students your age?<br \/>\nAnswer: 200 pages<\/p>\n<p>Question 18.<br \/>\nHow many hours do sixth-grade students use the Internet each week?<br \/>\nAnswer: 1.5 hour each<\/p>\n<p>Question 19.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe vertical dot plot shows the heights of the players on a recent NBA championship team.<br \/>\na. Find and interpret the number of data values on the dot plot.<br \/>\nb. How can you collect these data? What are the units?<br \/>\nc. Write a statistical question that you can answer using the dot plot. Then answer the question.<br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe dot plot shows the lengths of earthworms.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24120\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-14.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 14\" width=\"585\" height=\"192\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-14.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-14-300x98.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><br \/>\na. Find and interpret the number of data values on the dot plot.<br \/>\nAnswer: There are 21 data values on the plot.<br \/>\nb. How can you collect these data? What are the units?<br \/>\nAnswer: Based on dot plots and units are measured in mm.<br \/>\nc. Write a statistical question that you can answer using the dot plot. Then answer the question.<br \/>\nAnswer: Find the mode of the length of earthworms using the dot plot.<br \/>\n23 is repeated times.<br \/>\nSo, the mode is 23.<\/p>\n<p><strong>DESCRIBING DATA<\/strong><br \/>\nDisplay the data in a dot plot. Identify any clusters, peaks, or gaps in the data.<br \/>\nQuestion 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24121\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-15.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 15\" width=\"190\" height=\"130\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-56309\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/bim-grade-6-chapter-9-statictical-measures-answers-key-img_5-300x133.png\" alt=\"bim grade 6 chapter 9 statictical measures answers key img_5\" width=\"300\" height=\"133\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/bim-grade-6-chapter-9-statictical-measures-answers-key-img_5-300x133.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/bim-grade-6-chapter-9-statictical-measures-answers-key-img_5.png 448w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<div class=\"solution-cell explanation\" data-complete=\"complete\">\n<div class=\"solution-content\">\n<p class=\"center\">Data are clustered around 22 and around 25<br \/>\n<span style=\"font-size: 16px;\">Peak at 25<br \/>\n<\/span><span style=\"font-size: 16px;\">The gap between 16 and 21<\/span><\/p>\n<\/div>\n<\/div>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24122\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-16.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 16\" width=\"207\" height=\"121\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-56314\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/bim-grade-6-chapter-9-statictical-measures-answers-key-img_6-300x134.png\" alt=\"bim grade 6 chapter 9 statictical measures answers key img_6\" width=\"300\" height=\"134\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/bim-grade-6-chapter-9-statictical-measures-answers-key-img_6-300x134.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/bim-grade-6-chapter-9-statictical-measures-answers-key-img_6.png 444w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<div class=\"solution-cell explanation\" data-complete=\"complete\">\n<div class=\"solution-content\">\n<p class=\"center\">No clusters<br \/>\n<span style=\"font-size: 16px;\">Peak at 83<br \/>\n<\/span><span style=\"font-size: 16px;\">No gaps<\/span><\/p>\n<\/div>\n<\/div>\n<p><strong>INTERPRETING DATA<\/strong><br \/>\nThe dot plot shows the speeds of cars in a traffic study. Estimate the speed limit. Explain your reasoning.<br \/>\nQuestion 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24123\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-17.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 17\" width=\"307\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-17.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-17-300x75.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><br \/>\nAnswer: Most of the data clustered around 44 and 45 , hence the estimated speed is between 44-45 miles per hour<\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24124\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-18.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 18\" width=\"309\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-18.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-18-300x90.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\nAnswer: Most of the data clustered around 65 , there is a peak at 65 and gaps between&#8221;60-62&#8243; and 63-65.<\/p>\n<p>Question 25.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou conduct a survey to answer, \u201cHow many hours does a sixth-grade student spend on homework during a school night?\u201d The table shows the results.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24125\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.1-19.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.1 19\" width=\"120\" height=\"137\" \/><br \/>\na. Is this a statistical question? Explain.<br \/>\nAnswer: yes, it is a statistical question because students work in the different time zone based on individual student capacity.<br \/>\nb. Identify any clusters, peaks, or gaps in the data.<br \/>\nAnswer: cluster is around 2. There is a peak at 2 and there is no gap.<br \/>\nc. Use the distribution of the data to answer the question.<br \/>\nAnswer: A total of 29 data values are distributed.<\/p>\n<p><strong>RESEARCH<\/strong><br \/>\nUse the Internet to research and identify the method of measurement and the units used when collecting data about the topic.<br \/>\nQuestion 26.<br \/>\nwind speed<br \/>\nAnswer: The instruments used to measure wind are known as anemometers and can record wind speed, direction, and the strength of gusts. The normal unit of wind speed is the knot\u00a0(nautical mile per hour\u00a0= 0.51\u00a0m sec-1 = 1.15\u00a0mph).<\/p>\n<p>Question 27.<br \/>\namount of rainfall<br \/>\nAnswer:<br \/>\nThe standard instrument for the measurement of rainfall is the 203mm (8 inches) rain gauge. This is essentially a circular funnel with a diameter of 203mm which collects the rain into a graduated and calibrated cylinder. The measuring cylinder can record up to\u00a025mm\u00a0of precipitation<\/p>\n<p>Question 28.<br \/>\nearthquake intensity<br \/>\nAnswer: The\u00a0Richter scale\u00a0measures the largest wiggle (amplitude) on the recording, but other magnitude scales measure different parts of the earthquake. The USGS currently reports earthquake magnitudes using the\u00a0Moment Magnitude scale, though many other magnitudes are calculated for research and comparison purposes.<\/p>\n<p>Question 29.<br \/>\n<strong>REASONING<\/strong><br \/>\nWrite a question about letters in the English alphabet that is not a statistical question. Then write a question about letters that is a statistical question. Explain your reasoning.<br \/>\nAnswer: Statistical Question: How many letters in the English alphabet are used to spell a student&#8217;s name in class?<br \/>\nReasoning: The original question has one answer. This Question will have many answers.<\/p>\n<p>Question 30.<br \/>\n<strong>REASONING<\/strong><br \/>\nA bar graph shows the favorite colors of 30 people. Does it make sense to describe clusters in the data? peaks? gaps? Explain.<br \/>\nAnswer: No, It doesn&#8217;t make sense to describe the distribution. Colors are not measures numerically.<\/p>\n<h3><a id=\"Lesson_9.2_Mean\"><\/a>Lesson 9.2 Mean<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Finding a Balance Point<br \/>\nWork with a partner. The diagrams show the numbers of tokens brought to a batting cage. Where on the number line is the data set balanced ? Is this a good representation of the average? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24126\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-1.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 1\" width=\"532\" height=\"230\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-1.png 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-1-300x130.png 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Finding a Fair Share<br \/>\nWork with a partner. One token lets you hit 12 baseballs in a batting cage. The table shows the numbers of tokens six friends bring to the batting cage.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24127\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-2.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 2\" width=\"401\" height=\"92\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-2.png 401w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-2-300x69.png 300w\" sizes=\"(max-width: 401px) 100vw, 401px\" \/><br \/>\na. Regroup the tokens so that everyone has the same amount. How many times can each friend use the batting cage? Explain how this represents a \u201cfair share. &#8220;Use Clear De\ufb01nitions What does it mean for data to have an average? How does this help you answer the question?<br \/>\nb. how can you find the answer in part(a) algebraically?<br \/>\nc. Write a statistical question that can be answered using the value in part(a).<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-24128\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-3.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 3\" width=\"187\" height=\"80\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the mean of the data.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24131\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-6.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 6\" width=\"177\" height=\"228\" \/><br \/>\nAnswer:<br \/>\nThe sum of the data\/no of values<br \/>\nThe sum of the data=45+54+13+44+89+60+9+18;<br \/>\nno of values=8<br \/>\nThe sum of the data=332:no of values=8; 332\/8=41.5 is the mean of the data<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24132\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-7.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 7\" width=\"222\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-7.png 222w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-7-150x150.png 150w\" sizes=\"(max-width: 222px) 100vw, 222px\" \/><br \/>\nAnswer:<br \/>\n555 is mean for the above-given data.<\/p>\n<p>Question 3.<br \/>\n<strong>WHA IT?<\/strong><br \/>\nThe monthly rainfall in May was 0.5 inch in City A and 2 inches in City B. Does this a\ufb00ect your answer in Example 2? Explain.<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>NUMBER SENSE<\/strong><br \/>\nIs the mean always equal to a value in the data set? Explain.<br \/>\nAnswer: It is the value\u00a0that is most common. You will notice, however, that the\u00a0mean\u00a0is not often one of the actual\u00a0values\u00a0that you have observed in your\u00a0data set.\u00a0In addition, the mean\u00a0is the only measure of central tendency where the sum of the deviations of each\u00a0value\u00a0from the\u00a0mean\u00a0is\u00a0always\u00a0zero.<\/p>\n<p>Question 5.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain why the mean describes a typical value in a data set.<br \/>\nAnswer:<br \/>\nA measure of central tendency is a single\u00a0value\u00a0that attempts to\u00a0describe\u00a0a\u00a0set\u00a0of\u00a0data\u00a0by identifying the central position within that\u00a0set\u00a0of\u00a0data.\u00a0The mean\u00a0(often called\u00a0the average) is most likely the measure of central tendency that you are most familiar with, but there are others, such as the\u00a0median\u00a0and the mode.<\/p>\n<p>Question 6.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nWhat can you determine when the mean of one data set is greater than the mean of another data set? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n<strong>COMPARING MEANS<\/strong><br \/>\nCompare the means of the data sets.<br \/>\nData set A: 43, 32, 16, 41, 24, 19, 30, 27<br \/>\nData set B: 44, 18, 29, 24, 36, 22, 26, 21<br \/>\nAnswer:<br \/>\nAn outlier is a data value that is much greater or much less than the other values. When included in a data set, it can affect the mean.<\/p>\n<p>Question 8.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe monthly numbers of customers at a store in the first half of a year are 282, 270, 320, 351, 319, and 252. The monthly numbers of customers in the second half of the year are 211, 185, 192, 216, 168, and 144. Compare the mean monthly customers in the first half of the year with the mean monthly customers in the second half of the year.<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nThe table shows tournament finishes for a golfer. What place does the golfer typically finish in tournaments? Explain how you found your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24137\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-12.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 12\" width=\"175\" height=\"149\" \/><br \/>\nAnswer: Mean=sum of data\/number of data values<br \/>\nMean=118\/16<br \/>\nMean=7.375<br \/>\na. The golfer&#8217;s mean finish was about 7th<br \/>\nb. The finishes 37 and 26 are much greater than other finishes. They are outliers<\/p>\n<h3><a id=\"Mean_Homework_&amp;_Practice_9.2\"><\/a>Mean Homework &amp; Practice 9.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Determine whether the question is a statistical question. Explain.<\/strong><br \/>\nQuestion 1.<br \/>\nHow tall are sixth-grade students?<br \/>\nAnswer: The average\u00a0height\u00a0for a\u00a0sixth grader\u00a0(age 12) is about five feet. Girls tend to be about an inch\u00a0taller\u00a0on average. But there is a wide range. Any\u00a0height\u00a0from about 52 inches (4\u20324\u2033) to 65 inches (5\u20325\u2033) is in the normal range according to the CDC.<\/p>\n<p>Question 2.<br \/>\nHow many minutes are there in 1 Year?<br \/>\nAnswer:<br \/>\nAn average Gregorian year is 365.2425 days (52.1775 weeks, 8765.82 hours, 525949.2 minutes, or 31556952 seconds). For this calendar, a common year is 365 days (8760 hours, 525600 minutes, or 31536000 seconds), and a leap year is 366 days (8784 hours, 527040 minutes, or 31622400 seconds).<\/p>\n<p>Question 3.<br \/>\nHow many counties are in Tennessee?<br \/>\nAnswer: Tennessee&#8217;s\u00a095 counties\u00a0are divided into four TDOT regions. Regional offices are located in Jackson (Region 4), Nashville (Region 3), Chattanooga (Region 2), and Knoxville (Region 1).<\/p>\n<p>Question 4.<br \/>\nWhat is a student\u2019s favorite sport?<br \/>\nAnswer: cricket<\/p>\n<p><strong>Write the percent as a fraction or mixed number in simplest form.<\/strong><br \/>\nQuestion 5.<br \/>\n84%<br \/>\nAnswer:0.84<\/p>\n<p>Question 6.<br \/>\n71%<br \/>\nAnswer:0.71<\/p>\n<p>Question 7.<br \/>\n353%<br \/>\nAnswer:3.53<\/p>\n<p>Question 8.<br \/>\n0.2%<br \/>\nAnswer:0.002<\/p>\n<p><strong>Divide. Check your answer.<\/strong><br \/>\nQuestion 9.<br \/>\n11.7 \u00f7 9<br \/>\nAnswer:1.3<\/p>\n<p>Question 10.<br \/>\n\\(\\sqrt [ 5 ]{ 72.8 } \\)<br \/>\nAnswer: 2.35<\/p>\n<p>Question 11.<br \/>\n\\(\\sqrt [ 6.8 ]{ 28.56 } \\)<br \/>\nAnswer: <span style=\"font-size: 16px;\">1.63<\/span><\/p>\n<p>Question 12.<br \/>\n93 \u00f7 3.75<br \/>\nAnswer:24.8<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p>FINDING A FAIR SHARE Regroup the amounts so that each person has the same amount. What is the amount? (See Exploration 2, p. 419.)<br \/>\nQuestion 13.<br \/>\nDollars brought by friends to a fair: 11, 12, 12, 12, 12, 12, 13<br \/>\nAnswer:<br \/>\nGiven : 11,12,12,12,12,12,13.<br \/>\nMean=Sum of data\/number of data values<br \/>\nMean=84\/7<br \/>\nMean=12<br \/>\nAnswer = 12 dollars for each friend<\/p>\n<p>Question 14.<br \/>\nTickets earned by friends playing an arcade game: 0, 0, 0, 1, 1, 2, 3<br \/>\nAnswer:<br \/>\nGiven : 0,0,0,1,1,2,3.<br \/>\nMean=Sum of data\/number of data values<br \/>\nMean= 7\/7<br \/>\nMean=1<br \/>\nAnswer = 1 Tickets each friend<\/p>\n<p><strong>FINDING THE MEAN<\/strong><br \/>\nFind the mean of the data.<br \/>\nQuestion 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24138\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-13.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 13\" width=\"169\" height=\"155\" \/><br \/>\nAnswer: 2 is the mean of the data.<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24139\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-14.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 14\" width=\"206\" height=\"164\" \/><br \/>\nAnswer: 3 is the mean of the above-given data.<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24140\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-15.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 15\" width=\"184\" height=\"150\" \/><br \/>\nAnswer: 103 is the mean of the above-given data<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24141\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-16.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 16\" width=\"281\" height=\"147\" \/><br \/>\nAnswer: 14.8 is the mean of the above-given data.<\/p>\n<p>Question 19.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou and your friends are watching a television show. One of your friends asks, \u201cHow long are the commercial breaks during this show?\u201dBreak Times (minutes)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24142\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-17.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 17\" width=\"188\" height=\"71\" \/><br \/>\na. Is this a statistical question? Explain.<br \/>\nAnswer: Yes it is a statistical question.<\/p>\n<p>b.Use the mean of the values in the table to answer the question.<br \/>\nAnswer:<br \/>\nGiven the data,<br \/>\n4.2, 3.5, 4.55, 2.75, 2.25<br \/>\nx\u0304 = (4.2 + 3.5 + 4.55 + 2.75 + 2.25)\/5<br \/>\nx\u0304 = 17.25\/5<br \/>\n= 3.45<\/p>\n<p>Question 20.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe table shows the monthly rainfall amounts at a measuring station.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24143\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-18.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 18\" width=\"585\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-18.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-18-300x35.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><br \/>\na. What is the mean monthly rainfall?<br \/>\nAnswer:<br \/>\nx\u0304 = (22.5 + 1.51 + 1.86 + 2.06 + 3.48 + 4.47 + 3.37 + 5.40 + 5.45 + 4.34 + 2.64 + 2.14)\/12<br \/>\n= 33.54\/12<br \/>\n= 2.795<\/p>\n<p>b. Compare the mean monthly rainfall for the first half of the year with the mean monthly rainfall for the second half of the year.<br \/>\nAnswer:<br \/>\nMean:<br \/>\nx\u0304 = (22.5 + 1.51 + 1.86 + 2.06 + 3.48 + 4.47)\/6<br \/>\n= 15.6\/6<br \/>\n= 2.6<br \/>\nFor second 6 months:<br \/>\nx\u0304 = (3.37 + 5.40 + 5.45 + 4.34 + 2.64 + 2.14)\/6<br \/>\n= 23.34\/6<br \/>\n= 3.89<br \/>\nThe mean value of the second 6 months is greater than the first 6 months.<\/p>\n<p>Question 21.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nCreate two different data sets that have six values and a mean of 21.<br \/>\nAnswer:<br \/>\nMean of 21:<br \/>\nSet 1:<br \/>\n12, 31, 21, 24, 13, 25 for these numbers we can calculate the mean we get 21<br \/>\nSet 2:<br \/>\n12, 31, 20, 30, 10, 18 for these numbers we can calculate the mean we get 21<\/p>\n<p>Question 22.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe bar graph shows your cell phone data usage for five months. Describe how the outlier affects the mean. Then use the data to answer the statistical question, \u201cHow much cell phone data do you use in a month?\u201d<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24144\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-19.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 19\" width=\"348\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-19.png 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-19-300x140.png 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><br \/>\nAnswer: 288 is a lot less than the other data values so it is an outlier<br \/>\nMean with outlier=10\/5<br \/>\nMean with outlier = 2<br \/>\nMean without outlier = 6.18\/5<br \/>\nMean without outlier = 1.236<br \/>\nThe outlier causes the mean to be about 0.76 data usage.<\/p>\n<p style=\"text-align: left;\">Question 23.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe table shows the heights of the volleyball players on two teams. Compare the mean heights of the two teams. Do outliers affect either mean? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24145\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-20.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 20\" width=\"610\" height=\"232\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-20.png 610w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-20-300x114.png 300w\" sizes=\"(max-width: 610px) 100vw, 610px\" \/><br \/>\nAnswer:<br \/>\nDolphins=59+65+53+56+58+61+64+68+51+56+54+57=702<br \/>\nTotal no of observations=12;Mean=702\\12=58.5<br \/>\nTigers=63+68+66+58+54+55+61+62+53+70+64+64=683<br \/>\nTotal no of observations=12; Mean=683\/12=56.9<\/p>\n<p>Question 24.<br \/>\n<strong>REASONING<\/strong><br \/>\nUse a dot plot to explain why the mean of the data set below is the point where the data set is balanced.<br \/>\n11, 13, 17, 15, 12, 18, 12<br \/>\nAnswer:<br \/>\nmean = (11 + 13 + 17 + 15 + 18 + 12)\/6<br \/>\n= 86\/6<br \/>\n= 14.3<\/p>\n<p>Question 25.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nIn your class, 7 students do not receive a weekly allowance, 5 students receive $3, 7 students receive $5, 3 students receive $6, and 2 students receive $8.<br \/>\na. What is the mean weekly allowance? Explain how you found your answer.<br \/>\nb. A new student who joins your class receives a weekly allowance of $3.50. Without calculating, explain how this affects the mean.<br \/>\nAnswer:<br \/>\nGiven number of students receive no amount = 7<br \/>\nNumber of students receive $3 = 5<br \/>\nThen, total amount 5 students receive = 5 \u00d7 3 = $15<br \/>\nThen, total amount 7 students receive = 5 \u00d7 7 = $35<br \/>\nNumber of students receive $6 = 3<br \/>\nThen total amount 3 students receive = 6 \u00d7 3 = $18<br \/>\nNumber of students receive $8 = 2<br \/>\nThen, total amount 2 students receive = 2 \u00d7 8 = $16<br \/>\nNow, the total amount all students receive =<br \/>\n15 + 35 + 18 + 6 = 84<br \/>\nThe total students = 7 + 5 + 7 + 3 + 2 = 24<br \/>\nMean = total amount\/total amount = 84\/24 = $3.5<br \/>\nHence, the mean weekly allowance is $3.5<\/p>\n<p>Question 26.<br \/>\n<strong>PRECISION<\/strong><br \/>\nA collection of 8 geodes has a mean weight of 14 ounces. A different collection of 12 geodes has a mean weight of 14 ounces. What is the mean weight of the 20 geodes? Explain how you found your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24146\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-9.2-21.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures 9.2 21\" width=\"178\" height=\"134\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA collection of 8 geodes has a mean weight of 14 ounces.<br \/>\nA different collection of 12 geodes has a mean weight of 14 ounces.<br \/>\nTotal weight of the first 8 backpacks<br \/>\n8\u00d714<br \/>\n112 pounds<br \/>\nTotal weight of the second 12 backpacks<br \/>\n12\u00d79<br \/>\n108<br \/>\nTotal weight of the whole 20 backpacks<br \/>\n112+108<br \/>\n220<br \/>\nSo the mean weight of the 20 backpacks<br \/>\n220 \/ 20<br \/>\n11<\/p>\n<h3><a id=\"Lesson_9.3_Measures_of_Center\"><\/a>Lesson 9.3 Measures of Center<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Finding the Median<br \/>\nWork with a partner.<br \/>\na. Write the total numbers of letters in the first and last names of 15 celebrities, historical figures, or people you know. One person is already listed for you.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24147\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 1\" width=\"491\" height=\"369\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-1.png 491w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-1-300x225.png 300w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><\/p>\n<p>Dr. B. R. Ambedkar-8<br \/>\nOtto von Bismarck-15<br \/>\nA. P. J. Abdul Kalam-10<br \/>\nVallabhbhai Patel-16<br \/>\nAlexander Hamilton-17<br \/>\nJawaharlal Nehru -15<br \/>\nMother Teresa -12<br \/>\nThomas Jefferson-15<br \/>\nJ. R. D. Tata -4<br \/>\nIndira Gandhi -12<br \/>\nSachin Tendulkar-15<br \/>\nNapoleon Bonaparte-17<br \/>\nJohn Adams-9<br \/>\nKarl Marx-8<br \/>\nAndrew Jackson-13<br \/>\nb. Order the values in your data set from least to greatest. Then write the data on a strip of grid paper with 15 boxes.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24148\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-2.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 2\" width=\"258\" height=\"47\" \/><br \/>\nc. The middle value of the data set is called the median. The value (or values) that occur most often is called the mode. Find the median and the mode of your data set. Explain how you found your answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24149\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-3.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 3\" width=\"138\" height=\"120\" \/><br \/>\nd. Why are the median and the mode considered averages of a data set?<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-24150\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-4.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 4\" width=\"178\" height=\"112\" \/><\/p>\n<p>A measure of center is a measure that describes the typical value of a data set. The mean is one type of measure of center. Here are two others.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nFind the median and mode of the data.1, 2, 20, 4, 17, 8, 12, 9, 5, 20, 13<br \/>\nAnswer: Given the data,<br \/>\n1, 2, 20, 4, 17, 8, 12, 9, 5, 20, 13<br \/>\nFirst, write the numbers in the ascending or descending order.<br \/>\n1, 2, 4, 5, 8, 9, 12, 13, 17, 20, 20<br \/>\nThe Median is 9.<br \/>\nThe mode is 20 because it is repeated more than once.<\/p>\n<p>Question 2.<br \/>\n100, 75, 90, 80, 110, 102<br \/>\nAnswer:<br \/>\nGiven the data,<br \/>\n100, 75, 90, 80, 110, 102<br \/>\nFirst, write the numbers in the ascending or descending order.<br \/>\n75, 80, 90, 100, 102, 110<br \/>\n= (90+100)\/2<br \/>\n= 85<br \/>\nMode:<br \/>\nNo mode in the data.<\/p>\n<p>Question 3.<br \/>\nOne member of the class was absent and ends up voting for horror. Does this change the mode? Explain.<br \/>\nAnswer: No<\/p>\n<p>Question 4.<br \/>\nThe times (in minutes) it takes six students to travel to school are 8, 10, 10, 15, 20, and 45. Find the mean, median, and mode of the data with and without the outlier. Which measure does the outlier affect the most?<br \/>\nAnswer:<br \/>\nMedian:<br \/>\nWrite the numbers in ascending or descending order<br \/>\n8, 10, 10, 15, 20, and 45<br \/>\n= (10 + 15)\/2 = 25\/2 = 12.5<br \/>\nMode:<br \/>\n10 is the mode. Because it is the most repeated number.<br \/>\nMean:<br \/>\nAdding up the values and then dividing by the number of values.<br \/>\n= (8 + 10 + 10 + 15 + 20 + 45)\/6<br \/>\n= 108\/6<br \/>\n= 18<\/p>\n<p>Question 5.<br \/>\nWHAT IF?<br \/>\nThe store decreases the price of each video game by$3. How does this decrease affect the mean, median, and mode?<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 6.<br \/>\n<strong>FINDING MEASURES OF CENTER<\/strong><br \/>\nConsider the data set below.<br \/>\n15, 18, 13, 11, 12, 21, 9, 11<br \/>\na. Find the mean, median, and mode of the data.<\/p>\n<p>Answer:<br \/>\nGiven the data,<br \/>\n15, 18, 13, 11, 12, 21, 9, 11<br \/>\nx\u0304 = (15 + 18 + 13 + 11 + 12 + 21 + 9 + 11)\/8<br \/>\nx\u0304 = 110\/8<br \/>\nx\u0304 = 13.75<br \/>\nMedian:<br \/>\nWrite the numbers in ascending order and descending order.<br \/>\n9, 11, 11, 12, 13, 15, 18, 21<br \/>\n= (12 + 13)\/2<br \/>\n= 12.5<br \/>\nMode:<br \/>\n11 is the mode because this is repeated more than one time.<\/p>\n<p>b. Each value in the data set is decreased by 7. How does this change affect the mean, median, and mode?<br \/>\nAnswer:<br \/>\nEach value is decreased by 7 in the given data<br \/>\n8, 11, 6, 4, 5, 14, 2, 4<br \/>\nx\u0304 = (8 + 11 + 6 + 4 + 5 + 14 + 2 + 4)\/8<br \/>\nx\u0304 = 54\/8<br \/>\nx\u0304 = 6.75<\/p>\n<p>Question 7.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain why a typical value in a data set can be described by the median or the mode.<br \/>\nAnswer:<br \/>\nFor data from skewed distributions, the median is better than the mean because it isn&#8217;t influenced by extremely large values. The mode is the only measure you can use for nominal or categorical data that can&#8217;t be ordered<\/p>\n<p>Question 8.<br \/>\nHow does removing the outlier affect your answer in Example 5?<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nIt takes 10 contestants on a television show 43, 41, 62, 40, 44, 43, 44, 46, 45, and 41 seconds to cross a canyon on a zipline. Find the mean, median, and mode of the data with and without the outlier. Which measure does the outlier affect the most?<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nThe table shows the weights of several great white sharks. Use the data to answer the statistical question, \u201cWhat is the weight of a great white shark?\u201d<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24158\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-12.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 12\" width=\"599\" height=\"181\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-12.png 599w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-12-300x91.png 300w\" sizes=\"(max-width: 599px) 100vw, 599px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Measures_of_Center_Homework_&amp;_Practice_9.3\"><\/a>Measures of Center Homework &amp; Practice 9.3<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the mean of the data.<\/strong><br \/>\nQuestion 1.<br \/>\n1, 5, 8, 4, 5, 7, 6, 6, 2, 3<br \/>\nAnswer: 4.7<\/p>\n<p>Explanation:<br \/>\nGiven the data,<br \/>\n1, 5, 8, 4, 5, 7, 6, 6, 2, 3<br \/>\nx\u0304 = \u2211x\/n<br \/>\nx\u0304 = (1 + 5 + 8 + 4 + 5 + 7 + 6 + 6 + 2 + 3)\/16<br \/>\nx\u0304 = 49\/16<br \/>\nx\u0304 = 3.06<\/p>\n<p>Question 2.<br \/>\n9, 12, 11, 11, 10, 7, 4, 8<br \/>\nAnswer: 9<\/p>\n<p>Explanation:<br \/>\nGiven the data,<br \/>\n9, 12, 11, 11, 10, 7, 4, 8<br \/>\nx\u0304 = \u2211x\/n<br \/>\nx\u0304 = (9 + 12 + 11 + 11 + 10 + 7 + 4 + 8)\/8<br \/>\nx\u0304 = 72\/8<br \/>\nx\u0304 = 9<\/p>\n<p>Question 3.<br \/>\n26, 42, 31, 50, 29, 37, 44, 31<br \/>\nAnswer: 36.25<\/p>\n<p>Explanation:<br \/>\nGiven the data,<br \/>\n26, 42, 31, 50, 29, 37, 44, 31<br \/>\nx\u0304 = \u2211x\/n<br \/>\nx\u0304 = (26+42+31+50+29+37+44+31)\/8<br \/>\nx\u0304 = 290\/8<br \/>\nx\u0304 = 36.25<\/p>\n<p>Question 4.<br \/>\n53, 45, 43, 55, 28, 21, 61, 29, 24, 40, 27, 42<br \/>\nAnswer: 39<\/p>\n<p>Explanation:<br \/>\nGiven the data,<br \/>\n53, 45, 43, 55, 28, 21, 61, 29, 24, 40, 27, 42<br \/>\nx\u0304 = \u2211x\/n<br \/>\nx\u0304 = (53+45+43+55+28+21+61+29+24+40+27+42)\/12<br \/>\nx\u0304 = 468\/12<br \/>\nx\u0304 = 39<\/p>\n<p>Question 5.<br \/>\nA shelf in your room can hold at most 30 pounds. \ue033 ere are 12 pounds of books already on the shelf. Which inequality represents the number of pounds you can add to the shelf?<br \/>\nA. x &lt; 18<br \/>\nB. x \u2265 18<br \/>\nC. x \u2264 42<br \/>\nD. x \u2264 18<br \/>\nAnswer: x \u2264 18<\/p>\n<p>Explanation:<br \/>\n12+x \u2264 30<br \/>\n12+x -12 \u2264 30-12<br \/>\nx \u2264 18<\/p>\n<p><strong>Find the missing values in the ratio table. Then write the equivalent ratios.<\/strong><br \/>\nQuestion 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24159\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-13.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 13\" width=\"234\" height=\"64\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-58315\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-13.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-13\" width=\"234\" height=\"64\" \/><\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24160\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-14.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 14\" width=\"217\" height=\"66\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-58317\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-14.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-14\" width=\"217\" height=\"66\" \/><\/p>\n<p><strong>Find the surface area of the prism.<\/strong><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24161\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-15.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 15\" width=\"124\" height=\"129\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nl = 6m<br \/>\nw = 5m<br \/>\nh = 5m<br \/>\nWe know that,<br \/>\nSurface Area of the Prism = 2lw + 2lh + 2hw<br \/>\n= 2(6 \u00d7 5) + 2(6 \u00d7 8) + 2(8 \u00d7 5)<br \/>\n= 60 + 96 + 80<br \/>\n= 236 sq. meters<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24162\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-16.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 16\" width=\"157\" height=\"114\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nl = 4.5 ft<br \/>\nw = 2ft<br \/>\nh = 3.5ft<br \/>\nWe know that,<br \/>\nSurface Area of the Prism = 2lw + 2lh + 2hw<br \/>\n= 2(4.5 \u00d7 2) + 2(4.5 \u00d7 3.5) + 2(2 \u00d7 3.5)<br \/>\n= 18 + 31.5 + 14<br \/>\n= 63.5 sq. ft<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24163\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-17.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 17\" width=\"151\" height=\"118\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nl = 6 yd<br \/>\nw = 4 yd<br \/>\nh = 2 yd<br \/>\nWe know that,<br \/>\nSurface Area of the Prism = bh + 2lh + lb<br \/>\n= 2 \u00d7 4 + 2(6 \u00d7 5) + 6 \u00d7 2<br \/>\n= 8 + 60 + 12<br \/>\n= 80 sq. yards<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p>FINDING THE MEDIAN Use grid paper to find the median of the data. (See Exploration 1, p. 425.)<br \/>\nQuestion 11.<br \/>\n9, 7, 2, 4, 3, 5, 9, 6, 8, 0, 3, 8<br \/>\nAnswer:<br \/>\nFirst, arrange the numbers in ascending or descending order.<br \/>\n= 0, 2, 3, 3, 4, 5, 6, 7, 8, 8, 9, 9<br \/>\n= (5 + 6)\/2<br \/>\n= 11\/2<br \/>\n= 5.5<\/p>\n<p>Question 12.<br \/>\n16, 24, 13, 36, 22, 26, 22, 28, 25<br \/>\nAnswer:<br \/>\nFirst, arrange the numbers in ascending or descending order.<br \/>\n13, 16, 22, 22, 24, 25, 26, 28, 36<br \/>\n24 is the median.<br \/>\nThe median is the middle score in a set of given data.<\/p>\n<p><strong>FINDING THE MEDIAN AND MODE<\/strong><br \/>\nFind the median and mode of the data.<br \/>\nQuestion 13.<br \/>\n3, 5, 7, 9, 11, 3, 8<br \/>\nAnswer: The Median is 7; The Mode is 3.<br \/>\nGiven: 3, 5, 7, 9, 11, 3, 8<br \/>\nSorted list: 3,3,5,7,8,9,11<br \/>\nMedian is the middle number in a sorted list of numbers = 7<br \/>\nThe mode is the value that appears most frequently in a data set = 3<\/p>\n<p>Question 14.<br \/>\n14, 19, 16, 13, 16, 14<br \/>\nAnswer: The Median is 15; The Modes are 14 and 16.<br \/>\nGiven: 13,14,14,16,16,19<br \/>\nSorted list: 14, 19, 16, 13, 16, 14<br \/>\nMedian is the middle number in a sorted list of numbers = 15<br \/>\nThe mode is the value that appears most frequently in a data set = 14,16<\/p>\n<p>Question 15.<br \/>\n16. 93, 81, 94, 71, 89, 92, 94, 99<br \/>\nAnswer: The Median is 90.5; The Mode is 94.<br \/>\nGiven: 16, 93, 81, 94, 71, 89, 92, 94, 99<br \/>\nSorted list: 16,71,81,89,92,93,94,94,99<br \/>\nMedian is the middle number in a sorted list of numbers = 92<br \/>\nThe mode is the value that appears most frequently in a data set = 94<\/p>\n<p>Question 16.<br \/>\n44, 13, 36, 52, 19, 27, 33<br \/>\nAnswer: The Median is 33; There are no modes.<br \/>\nGiven: 44, 13, 36, 52, 19, 27, 33<br \/>\nSorted list: 13,19,27,33,36,44,52<br \/>\nMedian is the middle number in a sorted list of numbers = 33<br \/>\nThe mode is the value that appears most frequently in a data set = no mode<\/p>\n<p>Question 17.<br \/>\n12, 33, 18, 28, 29, 12, 17, 4, 2<br \/>\nAnswer: The Median is 17; The Modes are 12.<br \/>\nGiven: 12, 33, 18, 28, 29, 12, 17, 4, 2<br \/>\nSorted list: 2,4,12,12,17,18,28,29,33<br \/>\nMedian is the middle number in a sorted list of numbers = 17<br \/>\nThe mode is the value that appears most frequently in a data set = 12<\/p>\n<p>Question 18.<br \/>\n55, 44, 40, 55, 48, 44, 58, 67<br \/>\nAnswer:<br \/>\nThe Median is 51.5<br \/>\nThe Modes are 44 and 55.<br \/>\nGiven: 55, 44, 40, 55, 48, 44, 58, 67<br \/>\nSorted list: 40,44,44,48,55,55,58,67<br \/>\nMedian is the middle number in a sorted list of numbers = 51.5<br \/>\nThe mode is the value that appears most frequently in a data set = 44,55<\/p>\n<p>Question 19.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend finds the median of the data. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24164\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-18.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 18\" width=\"237\" height=\"101\" \/><br \/>\nAnswer: No, first the given data is arranged in ascending order then after median is to be found. The median is 55<\/p>\n<p><strong>FINDING THE MODE<\/strong><br \/>\nFind the mode of the data.<br \/>\nQuestion 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24165\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-19.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 19\" width=\"186\" height=\"222\" \/><br \/>\nAnswer: The modes are Black and Blue.<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24166\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-20.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 20\" width=\"234\" height=\"215\" \/><br \/>\nAnswer: The modes are singing, dancing, comedy.<\/p>\n<p>Question 22.<br \/>\n<strong>REASONING<\/strong><br \/>\nIn Exercises 20 and 21, can you \ufb01nd the mean and median of the data? Explain.<br \/>\nAnswer: <span style=\"font-size: 16px;\">You can&#8217;t find the mean and median in exercises 20 and 21.<br \/>\n<\/span><span style=\"font-size: 16px;\">The data set is not made up of numbers<\/span><\/p>\n<p><strong>FINDING MEASURES OF CENTER<\/strong><br \/>\nFind the mean, median, and mode of the data.<br \/>\nQuestion 23.<br \/>\n4.7, 8.51, 6.5, 7.42, 9.64, 7.2, 9.3<br \/>\nAnswer: Given: 4.7, 8.51, 6.5, 7.42, 9.64, 7.2, 9.3<br \/>\nSorted list: 4.7, 6.5, 7.2, 7.42, 8.51, 9.64<br \/>\nMean: x\u0304 = \u2211x\/n<br \/>\nx\u0304 = (4.7+6.5+7.2+7.42+8.51+9.64)\/6<br \/>\nx\u0304 = 43.97\/6<br \/>\nx\u0304 =7.32<br \/>\nMedian: 7.42.<br \/>\nMode: no mode.<\/p>\n<p>Question 24.<br \/>\n8\\(\\frac{1}{2}\\), 6\\(\\frac{5}{8}\\), 3\\(\\frac{1}{8}\\), 5\\(\\frac{3}{4}\\), 6\\(\\frac{5}{8}\\), 5\\(\\frac{1}{4}\\), 10\\(\\frac{5}{8}\\), 4\\(\\frac{1}{2}\\)<br \/>\nAnswer: Given: 8.5, 6.62, 3.12, 5.75, 6.62, 5.25, 10.62, 4.5<br \/>\nSorted list: 3.12, 4.5, 5.25, 5.75, 6.62, 6.62, 8.5, 10.62<br \/>\nMean: x\u0304 = \u2211x\/n<br \/>\nx\u0304 = (3.12, 4.5, 5.25, 5.75, 6.62, 6.62, 8.5, 10.62)\/8<br \/>\nx\u0304 =<br \/>\nx\u0304 =<br \/>\nMedian: 6.18<br \/>\nMode: 6.62<\/p>\n<p>Question 25.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe weights (in ounces) of several moon rocks are shown in the table. Find the mean, median, and mode of the weights.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24167\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-21.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 21\" width=\"230\" height=\"117\" \/><br \/>\nAnswer:<br \/>\nMean<br \/>\nx\u0304 = (2.2 + 2.2 + 3.2 + 2.4 + 2.8 + 3.4 + 2.6 + 3.0 + 2.5)\/9<br \/>\nMedian:<br \/>\nWrite the moon rock weights in ascending or descending order.<br \/>\n2.6 is the median<br \/>\nMode:<br \/>\n2.2 is repeated move times<br \/>\nSo, 2.2 is the mode.<\/p>\n<p><strong>REMOVING AN OUTLIER<\/strong> Find the mean, median, and mode of the data with and without the outlier. Which measure does the outlier affect the most?<br \/>\nQuestion 26.<br \/>\n45, 52, 17, 63, 57, 42, 54, 58<br \/>\nAnswer:<br \/>\nOutliners means removing of the small data value<br \/>\n17 is the outliner<br \/>\nx\u0304 = \u2211x\/n<br \/>\n= (45 + 52 + 17 + 63 + 57 + 42 + 54 + 58)\/8<br \/>\n= 388\/8 = 48.5<br \/>\nMean without outliner:<br \/>\n= (45 + 52 + 63 + 57 + 42 + 54 + 58)\/7<br \/>\n= 371\/7 = 53<br \/>\nMedian with outliner:<br \/>\n17, 42, 45, 52, 54, 57, 58, 63<br \/>\n= (52 + 54)\/2<br \/>\n= 106\/2<br \/>\n= 53<br \/>\nMedian without outliner:<br \/>\n42, 45, 52, 54, 57, 58, 63<br \/>\n54 is the median<br \/>\nMode:<br \/>\nThere is no change of value in the without outliner and with the outliner.<br \/>\nSo, there is no mode in the data values.<\/p>\n<p>Question 27.<br \/>\n85, 77, 211, 88, 91, 84, 85<br \/>\nAnswer:<br \/>\n77 is the outliner<br \/>\nMean with outliner:<br \/>\nx\u0304 = (85 + 77 + 211 + 88 + 91 + 84 + 85)\/7<br \/>\n=721\/7<br \/>\n= 103<br \/>\nMean without outliner:<br \/>\nx\u0304 = (85 + 211 + 88 + 91 + 84 + 85)\/6<br \/>\n= 644\/6<br \/>\n= 107<br \/>\nMedian with outliner:<br \/>\nWrite the data values in ascending or descending order.<br \/>\n77, 84, 85, 88, 91, 211<br \/>\n85 is the median.<br \/>\nMedian without outliner:<br \/>\n84, 85, 85, 88, 91, 211<br \/>\n= (85 + 88)\/2<br \/>\n= 173\/2<br \/>\n= 86.5<br \/>\nMode:<br \/>\nThere is no change of value in the without outliner and with the outliner.<br \/>\n85 is the mode.<\/p>\n<p>Question 28.<br \/>\n23, 73, 45, 27, 23, 25, 43, 45<br \/>\nAnswer:<br \/>\n73 is the outliner<br \/>\nMean with outliner:<br \/>\nMean = (23 + 45 + 27 + 23 + 25 + 43 + 45)<br \/>\n= 231\/7<br \/>\n= 33<br \/>\nMean with outliner:<br \/>\nMean = (23 + 45 + 27 + 23 + 25 + 43 + 45+ 73)<br \/>\n= 304\/8<br \/>\n= 38<\/p>\n<p>Question 29.<br \/>\n101, 110, 99, 100, 64, 112, 110, 111, 102<br \/>\nAnswer:<br \/>\n64 is the outliner<br \/>\nMean with outliner:<br \/>\nx\u0304 = (101 + 110 + 99 + 100 + 64 + 112 + 110 + 111 + 102)\/9<br \/>\n= 901\/9 = 101<br \/>\nMean with outliner:<br \/>\nx\u0304 = (101 + 110 + 99 + 100 + 112 + 110 + 111 + 102)\/8<br \/>\n= 755\/8<br \/>\n= 94.37<br \/>\nMedian:<br \/>\nWrite the data values in ascending or descending order<br \/>\n64, 99, 100, 101, 102, 110, 111, 112<br \/>\nMedian without outliner:<br \/>\n= (101 + 102)\/2<br \/>\n= 203\/2<br \/>\n= 101.5<br \/>\nMode:<br \/>\nMode with and without outliner = 110<\/p>\n<p>Question 30.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe table shows the monthly salaries for employees at a company.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24168\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-22.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 22\" width=\"252\" height=\"99\" \/><br \/>\na. Find the mean, median, and mode of the data.<br \/>\nb. Each employee receives a 5% raise. Find the mean, median, and mode of the data with the raise. How does this increase affect the mean, median, and mode of the data?<br \/>\nc. How are the mean, median, and mode of the monthly salaries related to the mean, median, and mode of the annual salaries?<br \/>\nAnswer:<\/p>\n<p><strong>CHOOSING A MEASURE OF CENTER<br \/>\n<\/strong>Find the mean, median, and mode of the data. Choose the measure that best represents the data. Explain your reasoning.<br \/>\nQuestion 31.<br \/>\n48, 12, 11, 45, 48, 48, 43, 32<br \/>\nAnswer:<br \/>\nWrite the data in ascending order or descending order.<br \/>\n11, 12, 32, 43, 45, 48, 48, 48<br \/>\n= (32 + 43)\/2<br \/>\n= 75\/2<br \/>\n= 37.5<br \/>\n48 is the mode of the data<\/p>\n<p>Question 32.<br \/>\n12, 13, 40, 95, 88, 7, 95<br \/>\nAnswer:<br \/>\nMean:<br \/>\nx\u0304 = \u2211x\/n<br \/>\n= (12 + 13 + 40 + 95 + 88 + 7 + 95)\/7<br \/>\n= 350\/7 = 50<br \/>\nMedian:<br \/>\n7, 12, 13, 40, 88, 95, 95<br \/>\n40 is the median<br \/>\nmode:<br \/>\n95 is the mode.<\/p>\n<p>Question 33.<br \/>\n2, 8, 10, 12, 56, 9, 5, 2, 4<br \/>\nAnswer:<br \/>\nMean:<br \/>\nx\u0304 = \u2211x\/n<br \/>\n= (2 + 8 + 10 + 12 + 56 + 9 + 5 + 2 + 4)\/9<br \/>\n= 108\/9<br \/>\n= 12<br \/>\nMedian:<br \/>\n2, 2, 4, 5, 8, 9, 10, 12, 56<br \/>\n8 is the median<br \/>\nMode:<br \/>\n2 is the mode.<\/p>\n<p>Question 34.<br \/>\n126, 62, 144, 81, 144, 103<br \/>\nAnswer:<br \/>\nMean:<br \/>\nx\u0304 = \u2211x\/n<br \/>\n= (126 + 62 + 144 + 81 + 144 + 103)6<br \/>\n= 660\/60<br \/>\n= 11<br \/>\nMedian:<br \/>\n62, 81, 103, 126, 144, 144<br \/>\n= (103 + 126)\/2<br \/>\n= 114.5<\/p>\n<p>Question 35.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe weather forecast for a week is shown. Which measure of center best represents the high temperatures? the low temperatures? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24169\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-23.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 23\" width=\"497\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-23.png 497w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-23-300x67.png 300w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 36.<br \/>\n<strong>RESEARCH<\/strong><br \/>\nFind the costs of 10 different boxes of cereal. Choose one cereal whose cost will be an outlier.<br \/>\na. Which measure of center does the outlier affect the most? Justify your answer.<br \/>\nb. Use the data to answer the statistical question, \u201cHow much does a box of cereal cost?\u201d<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe bar graph shows the numbers of hours you volunteered at an animal shelter. What is the minimum number of hours you need to volunteer in the seventh week to justify that you volunteered an average of 10 hours per week for the 7 weeks? Explain your answer using measures of center.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24170\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-24.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 24\" width=\"336\" height=\"226\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-24.png 336w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-24-300x202.png 300w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 38.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhy is the mode the least frequently used measure of center to describe a data set? Explain.<br \/>\nAnswer:<br \/>\nThe mode can be helpful in some analyses, but generally it does not contain enough accurate information to be useful in determining the shape of a distribution. When it is not a &#8220;Normal Distribution&#8221; the Mode can be misleading, although it is helpful in conjunction with the Mean for defining the amount of skewness in a distribution.<\/p>\n<p>Question 39.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe data are the prices of several fitness wristbands at a store.<br \/>\n$130 $170 $230 $130<br \/>\n$250 $275 $130 $185<br \/>\na. Does the price shown in the advertisement represent the prices well? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24171\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-9.3-25.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures 9.3 25\" width=\"262\" height=\"158\" \/><br \/>\nb. Why might the store use this advertisement?<br \/>\nc. In this situation, why might a person want to know the mean? the median? the mode? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 40.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nThe expressions 3x, 9x, 4x, 23x, 6x, and 3x form a data set. Assume x&gt; 0.<br \/>\na. Find the mean, median, and mode of the data.<br \/>\nb. Is there an outlier? If so, what is it?<br \/>\nAnswer:<br \/>\nMean: This is an average of all the numbers. Add up the numbers and then divide by how many numbers there are.<br \/>\n(3 + 9 + 4 + 23 + 6 + 3)\/6 = 48\/6 = 8<br \/>\nMedian: The number in the middle, when the numbers are in order. If there are 2 middle numbers, average them together.<br \/>\n3, 3, 4, 6, 9, 23 : 4 and 6 are the middle numbers. 4+6\/2 = 10\/2 = 5<br \/>\nMode: What value occurs most frequently? 3 is the only duplicate<br \/>\nOutlier: What value is abnormal to our set of data? All of our numbers are small (single digits), except for 23. That makes it an outlier.<\/p>\n<h3><a id=\"Lesson_9.4_Measures_of_Variation\"><\/a>Lesson 9.4 Measures of Variation<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Interpreting Statements<br \/>\nWork with a partner. There are 24 students in your class. Your teacher makes the following statements.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24172\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-1.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 1\" width=\"485\" height=\"154\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-1.png 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-1-300x95.png 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><br \/>\n\u2022 \u201cThe exam scores range from 75% to 96%.\u201d<br \/>\na. What does each statement mean? Explain.<br \/>\nb. Use your teacher\u2019s statements to make a dot plot that can represent the distribution of the exam scores of the class.<br \/>\nc. Compare your dot plot with other groups\u2019. How are they alike? different?<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Grouping Data<br \/>\nWork with a partner. The numbers of U.S.states visited by students in a sixth-grade class are shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24173\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-2.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 2\" width=\"563\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-2.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-2-300x93.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><br \/>\na. Represent the data using a dot plot. Between what values do the data range?<br \/>\nb. Use the dot plot to make observations about the data.<br \/>\nc. How can you describe the middle half of the data?<\/p>\n<p>A measure of variation is a measure that describes the distribution of a data set. A simple measure of variation to find is the range. The range of a data set is the difference of the greatest value and the least value.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-24174\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-3.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 3\" width=\"181\" height=\"184\" \/><\/p>\n<p><strong>Try It<br \/>\n<\/strong>Question 1.<br \/>\nThe ages of people in line for a roller coaster are 15, 17, 21, 32, 41, 30, 25, 52, 16, 39, 11, and 24. Find and interpret the range of the ages.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nThe ages of people in line for a roller coaster are 15, 17, 21, 32, 41, 30, 25, 52, 16, 39, 11, and 24.<br \/>\nRange = (upper value &#8211; lower value)\/2<br \/>\n= (52 &#8211; 11)\/2<br \/>\n= 41\/2<br \/>\n= 20.5<\/p>\n<p>Question 2.<br \/>\nThe data are the number of pages in each of an author\u2019s novels. Find and interpret the interquartile range of the data.<br \/>\n356, 364, 390, 468, 400, 382, 376, 396, 350<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nThe data are the number of pages in each of an author\u2019s novels.<br \/>\n356, 364, 390, 468, 400, 382, 376, 396, 350<br \/>\nLower quartile = 360<br \/>\nUpper quartile = 398<br \/>\nInterquartile range = 38<\/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 why the variability of a data set can be described by the range or the interquartile range.<br \/>\nAnswer:<br \/>\nThe interquartile range is the third quartile (Q3) minus the first quartile (Q1). But the IQR is less affected by outliers: the 2 values come from the middle half of the data set, so they are unlikely to be extreme scores. The IQR gives a consistent measure of variability for skewed as well as normal distributions.<\/p>\n<p>Question 4.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24179\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-8.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 8\" width=\"524\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-8.png 524w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-8-300x102.png 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nThe table shows the distances traveled by a paper airplane. Find and interpret the range and interquartile range of the distances.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24182\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-11.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 11\" width=\"178\" height=\"163\" \/><br \/>\nAnswer: Given: 13.5, 12.5, 21, 16.75, 10.25, 19, 32, 26.5, 29,16.25, 28.5, 18.5.<\/p>\n<p>Question 6.<br \/>\nThe table shows the years of teaching experience of math teachers at a school. How do the outlier or outliers affect the variability of the data?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24183\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-12.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 12\" width=\"330\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-12.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-12-300x61.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\nAnswer:<br \/>\nGiven the data<br \/>\n5, 10, 7, 8, 10, 11, 22, 8, 6, 35<br \/>\n22 is added to the data set<br \/>\n22 is the outliner<br \/>\nso there is no effect to measure of center and the measure of variability.<\/p>\n<h3><a id=\"Measures_of_Variation_Homework_&amp;_Practice_9.4\"><\/a>Measures of Variation Homework &amp; Practice 9.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the mean, median, and mode of the data.<\/strong><br \/>\nQuestion 1.<br \/>\n4, 8, 11, 6, 4, 5, 9, 10, 10, 4<br \/>\nAnswer:<br \/>\nMean = x\u0304 = (4 + 8 + 11 + 6 + 4 + 5 + 9 + 10 + 10 + 4)\/10<br \/>\n= 71\/10<br \/>\n= 7.1<br \/>\nMedian:<br \/>\nWrite the data in ascending or descending order.<br \/>\n4, 4, 4, 5, 6, 8, 9, 10, 10, 11<br \/>\n= (5 + 8)\/2<br \/>\n= 13\/2<br \/>\n=6.5<br \/>\nMode:<br \/>\nMore number if data repeated is called mode.<br \/>\n4 is the mode.<\/p>\n<p>Question 2.<br \/>\n74, 78, 86, 67, 80<br \/>\nAnswer:<br \/>\nMean = x\u0304 = (74 + 78 + 86 + 67 + 80)\/5<br \/>\n= 385\/5<br \/>\n= 77<br \/>\nMedian:<br \/>\nWrite the data in ascending or descending order.<br \/>\n67, 74, 78, 80, 86<br \/>\n78 is the median<br \/>\nMode:<br \/>\nThere is no mode in the data.<\/p>\n<p>Question 3.<br \/>\n15, 18, 17, 17, 15, 16, 14<br \/>\nAnswer:<br \/>\nMean = x\u0304 = (15 + 18 + 17 + 17 + 15 + 16 + 14)\/7<br \/>\n= 112\/7 = 16<br \/>\nMedian:<br \/>\nWrite the data in ascending or descending order.<br \/>\n14, 15, 15, 16, 17, 17, 18<br \/>\n16 is the median<br \/>\nMode:<br \/>\n17, 15 are the median.<\/p>\n<p>Question 4.<br \/>\n31, 14, 18, 26, 17, 32<br \/>\nAnswer:<br \/>\nMean:<br \/>\nx\u0304 = (31 + 14 + 18 + 26 + 17 + 32)\/6<br \/>\nMedian:<br \/>\nWrite the data in ascending or descending order.<br \/>\n14, 17, 18, 26, 31, 32<br \/>\n= (18 + 26)\/2<br \/>\n= 44\/2<br \/>\n= 22<br \/>\nMode:<br \/>\nThere is no mode in the data.<\/p>\n<p><strong>Copy and complete the statement using &lt; or &gt;.<\/strong><br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24184\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-13.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 13\" width=\"70\" height=\"28\" \/><br \/>\nAnswer:<br \/>\nA negative number is less than the positive number<br \/>\n6 &gt; -7<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24185\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-14.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 14\" width=\"73\" height=\"38\" \/><br \/>\nAnswer:<br \/>\nA negative number is less than the positive number<br \/>\n-3 &lt; 0<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24186\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-15.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 15\" width=\"82\" height=\"33\" \/><br \/>\nAnswer:<br \/>\nA negative number is less than the positive number<br \/>\n14 &gt; -14<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24187\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-16.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 16\" width=\"82\" height=\"35\" \/><br \/>\nAnswer:<br \/>\nA negative number is less than the positive number<br \/>\n8 &gt; -10<\/p>\n<p><strong>Find the surface area of the pyramid.<\/strong><br \/>\nQuestion 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24188\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-17.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 17\" width=\"137\" height=\"126\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nLength = 12 mm<br \/>\nHeight = 14 mm<br \/>\nA = a\u00b2 + 2a \u221aa\u00b2\/4 + h\u00b2<br \/>\nArea = 509.56 sq. mm<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24189\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-18.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 18\" width=\"127\" height=\"134\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nLength = 5 in<br \/>\nHeight = 8.5 in<br \/>\nA = a\u00b2 + 2a \u221aa\u00b2\/4 + h\u00b2<br \/>\nArea = 113.6 sq. inches<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24190\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-19.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 19\" width=\"122\" height=\"132\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nLength = 6 ft<br \/>\nHeight = 9 ft<br \/>\nA = a\u00b2 + 2a \u221aa\u00b2\/4 + h\u00b2<br \/>\nArea = 149.84 sq.ft<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>INTERPRETING STATEMENTS<\/strong> There are 20 students in your class. Your teacher makes the two statements shown. Use your teacher\u2019s statements to make a dot plot that can represent the distribution of the scores of the class. (See Exploration 1, p. 433.)<br \/>\nQuestion 12.<br \/>\n\u201cThe quiz scores range from 65% to 95%.\u201d<br \/>\n\u201cThe scores were evenly spread out.\u201d<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n\u201cThe project scores range from 78% to 93%.\u201d<br \/>\n\u201cMost of the students received low scores.\u201d<br \/>\nAnswer:<\/p>\n<p><strong>FINDING THE RANGE<\/strong> Find the range of the data.<br \/>\nQuestion 14.<br \/>\n4, 8, 2, 9, 5, 3<br \/>\nAnswer: 7<\/p>\n<p>Explanation:<br \/>\nRange is the difference of higher value and lower value<br \/>\nlowest value = 2<br \/>\nhighest value = 9<br \/>\nR = 9 &#8211; 2<br \/>\nR = 7<\/p>\n<p>Question 15.<br \/>\n28, 42, 36, 23, 14, 47, 40<br \/>\nAnswer: 33<\/p>\n<p>Explanation:<br \/>\nThe range is the difference between higher value and lower value<br \/>\nLowest value: 14<br \/>\nHighest value: 47<br \/>\nRange = 47 &#8211; 14<br \/>\nR = 33<\/p>\n<p>Question 16.<br \/>\n26, 21, 27, 33, 24, 29<br \/>\nAnswer: 12<\/p>\n<p>Explanation:<br \/>\nThe range is the difference between higher value and lower value<br \/>\nLowest value: 21<br \/>\nHighest value: 33<br \/>\nRange = 33 &#8211; 21<br \/>\nR = 12<\/p>\n<p>Question 17.<br \/>\n52, 40, 49, 48, 62, 54, 44, 58, 39<br \/>\nAnswer: 23<\/p>\n<p>Explanation:<br \/>\nThe range is the difference between higher value and lower value<br \/>\nLowest value: 39<br \/>\nHighest value: 62<br \/>\nRange = 62 &#8211; 39<br \/>\nR = 23<\/p>\n<p>Question 18.<br \/>\n133, 117, 152, 127, 168, 146, 174<br \/>\nAnswer: 57<\/p>\n<p>Explanation:<br \/>\nThe range is the difference between higher value and lower value<br \/>\nLowest value: 117<br \/>\nHighest value: 174<br \/>\nRange = 174 &#8211; 117<br \/>\nR = 57<\/p>\n<p>Question 19.<br \/>\n4.8, 5.5, 4.2, 8.9, 3.4, 7.5, 1.6, 3.8<br \/>\nAnswer: 7.3<\/p>\n<p>Explanation:<br \/>\nThe range is the difference of higher value and lower value<br \/>\nLowest value: 1.6<br \/>\nHighest value: 8.9<br \/>\nRange = 8.9 &#8211; 1.6<br \/>\nR = 7.3<\/p>\n<p>Question 20.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend finds the range of the data. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24191\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-20.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 20\" width=\"233\" height=\"104\" \/><br \/>\nAnswer:<br \/>\nThe range is the difference between higher value and lower value<br \/>\nLowest value: 28<br \/>\nHighest value: 59<br \/>\nRange =\u00a0 59 &#8211; 28<br \/>\nRange = 31<\/p>\n<p><strong>FINDING THE INTERQUARTILE RANGE<\/strong> Find the interquartile range of the data.<br \/>\nQuestion 21.<br \/>\n4, 6, 4, 2, 9, 1, 12, 7<br \/>\nAnswer: 6<\/p>\n<p>Explanation:<br \/>\nThis simple formula is used for calculating the interquartile range:<br \/>\nIQR = Xu &#8211; Xl<br \/>\nLower quartile (xL): 2.5<br \/>\nUpper quartile (xU): 8.5<br \/>\nIQR = 8.5 &#8211; 2.5<br \/>\nIQR = 6<\/p>\n<p>Question 22.<br \/>\n18, 22, 15, 16, 15, 13, 19, 18<br \/>\nAnswer: 3.75<\/p>\n<p>Explanation:<br \/>\nThis simple formula is used for calculating the interquartile range:<br \/>\nIQR = Xu &#8211; Xl<br \/>\nLower quartile (xL): 15<br \/>\nUpper quartile (xU): 18.75<br \/>\nIQR = 18.75 &#8211; 15<br \/>\n= 3.75<\/p>\n<p>Question 23.<br \/>\n40, 33, 37, 54, 41, 34, 27, 39, 35<br \/>\nAnswer: 7<\/p>\n<p>Explanation:<br \/>\nThis simple formula is used for calculating the interquartile range:<br \/>\nIQR = Xu &#8211; Xl<br \/>\nLower quartile (xL): 33.5<br \/>\nUpper quartile (xU): 40.5<br \/>\nIQR = 40.5 &#8211; 33.5<br \/>\n= 7<\/p>\n<p>Question 24.<br \/>\n84, 75, 90, 87, 99, 91, 85, 88, 76, 92, 94<br \/>\nAnswer: 8<\/p>\n<p>Explanation:<br \/>\nThis simple formula is used for calculating the interquartile range:<br \/>\nIQR = Xu &#8211; Xl<br \/>\nLower quartile (xL): 84<br \/>\nUpper quartile (xU): 92<br \/>\nIQR = 92 &#8211; 84<br \/>\n= 8<\/p>\n<p>Question 25.<br \/>\n132, 127, 106, 140, 158, 135, 129, 138<br \/>\nAnswer: 12<\/p>\n<p>Explanation:<br \/>\nThis simple formula is used for calculating the interquartile range:<br \/>\nIQR = Xu &#8211; Xl<br \/>\nLower quartile (xL): 127.5<br \/>\nUpper quartile (xU): 139.5<br \/>\nIQR = 139.5 &#8211; 127.5<br \/>\n= 12<\/p>\n<p>Question 26.<br \/>\n38, 55, 61, 56, 46, 67, 59, 75, 65, 58<br \/>\nAnswer: 12.75<\/p>\n<p>Explanation:<br \/>\nThis simple formula is used for calculating the interquartile range:<br \/>\nIQR = Xu &#8211; Xl<br \/>\nLower quartile (xL): 52.75<br \/>\nUpper quartile (xU): 65.5<br \/>\nIQR = 65.5\u00a0 &#8211; 52.75<br \/>\n= 12.75<\/p>\n<p>Question 27.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe table shows the number of tornadoes in Alabama each year for several years. Find and interpret the range and interquartile range of the data. Then determine whether there are any outliers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24192\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-21.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 21\" width=\"327\" height=\"209\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-21.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-21-300x192.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\nAnswer:<br \/>\nThe data is 65, 32, 54, 23, 55, 145,37, 80, 94, 42, 69, 77<br \/>\nRange:<br \/>\nLowest value: 23<br \/>\nHighest value: 145<br \/>\nR = Highest value &#8211; Lowest value<br \/>\nR = 145 &#8211; 23<br \/>\nR = 122<br \/>\nIQR:<br \/>\nThis simple formula is used for calculating the interquartile range:<br \/>\nIQR = Xu &#8211; Xl<br \/>\nLower quartile (xL): 38.25<br \/>\nUpper quartile (xU): 79.25<br \/>\nIQR = 79.25 &#8211; 38.25<br \/>\n= 41<\/p>\n<p>Question 28.<br \/>\n<strong>WRITING<\/strong><br \/>\nConsider a data set that has no mode. Which measure of variation is greater, the range or the interquartile range? Explain your reasoning.<br \/>\nAnswer:<br \/>\nIt would be based on the set of numbers you have, but in most cases, it is the interquartile range, because the mode is usually closer to the median. This leaves the interquartile range as a larger number.<\/p>\n<p>Question 29.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIs it possible for the range of a data set to be equal to the interquartile range? Explain your reasoning.<br \/>\nAnswer:<br \/>\nThe interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles. Quartiles divide a rank-ordered data set into four equal parts.<\/p>\n<p>Question 30.<br \/>\n<strong>REASONING<\/strong><br \/>\nHow does an outlier affect the range of a data set? Explain.<br \/>\nAnswer:<br \/>\nOutlier An extreme value in a set of data that is much higher or lower than the other numbers. Outliers affect the mean value of the data but have little effect on the median or mode of a given set of data.<\/p>\n<p>Question 31.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe table shows the numbers of points scored by players on a sixth-grade basketball team in a season.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24193\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-22.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 22\" width=\"406\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-22.png 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-22-300x67.png 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\na. Find the range and interquartile range of the data.<br \/>\nb. Identify the outlier(s) in the data set. Find the range and interquartile range of the data set without the outlier(s). Which measure does the outlier or outliers affect more?<br \/>\nAnswer:<\/p>\n<p>Question 32.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nTwo data sets have the same range. Can you assume that the interquartile ranges of the two data sets are about the same? Give an example to justify your answer.<br \/>\nAnswer:<br \/>\nYes,<br \/>\nA data set with the least value of 2 and the greatest value of 20 will have the same range as a data set with the least value of 82 and the greatest value of 100 will have the same range of 18.<\/p>\n<p>Question 33.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe tables show the ages of the finalists for two reality singing competitions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24194\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-23.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 9 Statistical Measures 9.4 23\" width=\"404\" height=\"264\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-23.png 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-9-Statistical-Measures-9.4-23-300x196.png 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><br \/>\na. Find the mean, median, range, and interquartile range of the ages for each show. Compare the results.<\/p>\n<p>Answer:<br \/>\n18, 15, 22, 18, 24, 17, 21, 16, 28, 21<br \/>\nMean:<br \/>\nx\u0304 = \u2211x\/n = (18 + 15 + 22 + 18 + 24 + 17 + 21 + 16 + 28 + 21)\/10<br \/>\n=200\/10 = 20<br \/>\nMedian:<br \/>\n15, 16,\u00a0 17,\u00a0 18,\u00a0 18, 21, 22, 24, 28<br \/>\n= (18 + 21)\/2<br \/>\n= 39\/2<br \/>\n= 19.5<br \/>\nRange:<br \/>\n(28 &#8211; 15)\/2<br \/>\n= 13\/2<br \/>\n= 6.5<br \/>\ninterquartile range:<br \/>\nNumber of observations: 10<br \/>\nXl = 16.75<br \/>\nXu = 22.5<br \/>\nXu &#8211; Xl = 5.75<br \/>\nAges of show B:<br \/>\nMean:<br \/>\nx\u0304 = \u2211x\/n = (21 + 20 + 23 + 13 + 15 + 18 + 17 + 22 + 36 + 25)\/10<br \/>\n= 210\/10 = 21<br \/>\nMedian:<br \/>\n13, 15, 17, 18, 20, 21, 22, 23, 25, 36<br \/>\n= (20 + 21)\/2 = 41\/2 = 20.5<br \/>\nRange:<br \/>\n(36 &#8211; 13)\/2<br \/>\n= 23\/2<br \/>\n= 11.5<br \/>\nInterquartile Range:<br \/>\nSamples = 10<br \/>\nXl = 16.5<br \/>\nXu = 23.5<\/p>\n<p>b. A 21-year-old is voted off Show A, and the 36-year-old is voted off Show B. How do these changes affect the measures in part(a)? Explain.<br \/>\nAnswer:<br \/>\nMean:<br \/>\nx\u0304 = \u2211x\/n = (18 + 17 + 15 + 22 + 16 + 18 + 28 + 24)\/8<br \/>\n= 158\/8<br \/>\n= 79<br \/>\nMedian: 15, 16, 17, 18, 18, 22, 24, 28<br \/>\n(18 + 18)\/2<br \/>\n= 36\/2<br \/>\n= 18<br \/>\nRange:<br \/>\n(28 &#8211; 15)\/2<br \/>\n= 13\/2<br \/>\n= 6.5<br \/>\nInterquartile Range:<br \/>\nSamples = 8<br \/>\nXl = 16.25<br \/>\nXu = 23.5<br \/>\nInterquartile Range = 23.5 &#8211; 16.25<br \/>\n= 7.25<br \/>\n21, 20, 23, 13, 15, 18, 17, 22, 25<br \/>\nMean = (21 + 20 + 23 + 13 + 15 + 18 + 17 + 22 + 25)\/9<br \/>\n= 174\/2<br \/>\n= 87<br \/>\nMedian:<br \/>\n13, 15, 17, 18, 21, 20, 22, 23, 25<br \/>\n21 is the median<br \/>\nRange:<br \/>\n(25 &#8211; 13)\/2<br \/>\n= 12\/2<br \/>\n= 6<br \/>\nInterquartile Range:<br \/>\ndata = 9<br \/>\nXl = 16<br \/>\nXu = 22.5<br \/>\n(Xu &#8211; Xl) = 22.5 &#8211; 16<br \/>\n= 6.5<br \/>\nIn Part A there is no effect on the range and it affects the mean, median, interquartile.<\/p>\n<p>Question 34.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nCreate a set of data with 7 values that has a mean of 30, a median of 26, a range of 50, and an interquartile range of 36.<br \/>\nAnswer:<br \/>\nThe first thing we need to do is to put the data in increasing order. This is needed to calculate the median:<br \/>\n30,31,32,33,34,35,35,36,37,39<\/p>\n<h3><a id=\"Lesson_9.5_Mean_Absolute_Deviation\"><\/a>Lesson 9.5 Mean Absolute Deviation<\/h3>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-24199\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.5-1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 1\" width=\"507\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.5-1.png 507w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.5-1-300x125.png 300w\" sizes=\"(max-width: 507px) 100vw, 507px\" \/><\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Finding Distances from the Mean<br \/>\nWork with a partner. The table shows the exam scores of 14 students in your class.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24200\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.5-2.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 2\" width=\"564\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.5-2.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.5-2-300x94.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><br \/>\na. Which exam score deviates the most from the mean? Which exam score deviates the least from the mean? Explain how you found your answers.<br \/>\nb. How far is each data value from the mean?<br \/>\nc. Divide the sum of the values in part(b) by the number of values. In your own words, what does this represent?<br \/>\nd. REASONING Ina data set, what does it mean when the value you found in part(c) is close to 0? Explain.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-24201\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.5-3.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 3\" width=\"188\" height=\"88\" \/><\/p>\n<p>Another measure of variation is the mean absolute deviation. The mean absolute deviation is an average of how much data values differ from the mean.<\/p>\n<p><strong>Try It<\/strong><br \/>\nQuestion 1.<br \/>\nFind and interpret the mean absolute deviation of the data.<br \/>\n5, 8, 8, 10, 13, 14, 16, 22<br \/>\nAnswer: Number of observations : 8<br \/>\nMean: 12<\/p>\n<p>Question 2.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nThe pitcher allows 4 runs in the next game. How would you expect the mean absolute deviation to change? Explain.<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 why the variability of a data set can be described by the mean absolute deviation.<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n<strong>FINDING THE MEAN ABSOLUTE DEVIATION<\/strong><br \/>\nFind and interpret the mean absolute deviation of the data. 8, 12, 4, 3, 14, 1, 9, 13<br \/>\nAnswer: number of observations:8<br \/>\nMean: 8<br \/>\nmean absolute deviation: 4<\/p>\n<p>Question 5.<br \/>\n<strong>WHICH ONE do DOESN\u2019T BELONG?<\/strong><br \/>\nWhich one does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24204\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.5-6.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 6\" width=\"298\" height=\"80\" \/><br \/>\nAnswer: MEAN<br \/>\nA mean is different from all the above-given factors<br \/>\nA\u00a0mean\u00a0is the simple mathematical average of a set of two or more numbers.<br \/>\nThe\u00a0mean\u00a0for a given set of numbers can be computed in more than one way, including the arithmetic\u00a0mean\u00a0method, which uses the sum of the numbers in the series, and the geometric\u00a0mean method, which is the average of a set of products.<\/p>\n<p>Question 6.<br \/>\nThe tables show the numbers of questions answered correctly by members of two teams on a game show. Compare the mean, median, and mean absolute deviation of the numbers of correct answers for each team. What can you conclude?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24207\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.5-9.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 9\" width=\"223\" height=\"185\" \/><br \/>\nAnswer:<br \/>\nTiger sharks<br \/>\n3, 6, 5, 4, 4, 2<br \/>\nMean: (3 + 6 + 5 + 4 + 4 + 2)\/6<br \/>\n= 24\/6<br \/>\n= 4<br \/>\nMedian:<br \/>\n2, 3, 4, 4, 5, 6<br \/>\n= (4 + 4)\/2<br \/>\n= 4<br \/>\nMAD:<br \/>\nNumber of observations: 6<br \/>\nMean = 4<br \/>\nMAD = 1<br \/>\nBear Cats:<br \/>\nMean:<br \/>\n6, 1, 4, 1, 8, 4<br \/>\n(6 + 1 + 4 + 1 + 8 + 4)\/6<br \/>\n= 24\/6<br \/>\n= 4<br \/>\nMedian:<br \/>\n1, 1, 4, 4, 6, 8<br \/>\n= (4 + 4)\/2<br \/>\n= 4<br \/>\nMAD:<br \/>\nNumber of observations: 6<br \/>\nMean = 4<br \/>\nMAD = 2<br \/>\nThe mean, Median, Mean Absolute Deviation of both tiger sharks and Bear Cats are the same.<\/p>\n<p>Question 7.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe data set shows the numbers of books that students in your book club read last summer.<br \/>\n8, 6, 11, 12, 14, 12, 11, 6, 15, 9, 7, 10, 9, 13, 5, 8<br \/>\nA new student who read 18 books last summer joins the club. Is18 an outlier? How does including this value in the data set a\ufb00ect the measures of center and variation? Explain.<br \/>\nAnswer: 8 is added to the dataset.<br \/>\nYes, 18 is an outliner<br \/>\nNo, it does not affect the measures of the center and variation by removing the outliner.<br \/>\nIf the outliner is not removed then it affects the measures of center and variation.<\/p>\n<h3><a id=\"Mean_Absolute_Deviation_Homework_&amp;_Practice_9.5\"><\/a>Mean Absolute Deviation Homework &amp; Practice 9.5<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the range and interquartile range of the data.<\/strong><br \/>\nQuestion 1.<br \/>\n23, 45, 39, 34, 28, 41, 26, 33<br \/>\nAnswer:<br \/>\nNumber of observations:8<br \/>\nLower quartile (xL): 26.5<br \/>\nUpper quartile (xU): 40.5<br \/>\ninterquartile range = 14<br \/>\nRange:<br \/>\nNumber of observations:8<br \/>\nLowest value: 23<br \/>\nHighest value: 45<br \/>\nRange = 45 &#8211; 23<br \/>\n= 22<\/p>\n<p>Question 2.<br \/>\n63, 53, 48, 61, 69, 63, 57, 72, 46<br \/>\nAnswer:<br \/>\nNumber of observations:9<br \/>\nLower quartile (xL): 50.5<br \/>\nUpper quartile (xU): 66<br \/>\ninterquartile range = 15.5<br \/>\nRange:<br \/>\nNumber of observations:9<br \/>\nLowest value: 46<br \/>\nHighest value: 72<br \/>\nRange = 26<\/p>\n<p><strong>Graph the integer and its opposite.<\/strong><br \/>\nQuestion 3.<br \/>\n15<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-60050\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-9-Statistics-Answer-Key-img_5-300x76.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 9 Statistics Answer Key img_5\" width=\"300\" height=\"76\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-9-Statistics-Answer-Key-img_5-300x76.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-9-Statistics-Answer-Key-img_5.jpg 645w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 4.<br \/>\n17<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-60073\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-9-Statistics-Answer-Key-img_6-300x78.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 9 Statistics Answer Key img_6\" width=\"300\" height=\"78\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-9-Statistics-Answer-Key-img_6-300x78.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-9-Statistics-Answer-Key-img_6.jpg 645w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 16.<br \/>\n&#8211; 22<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-60075\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-9-Statistics-Answer-Key-img_7-300x110.png\" alt=\"Big Ideas Math Grade 6 Chapter 9 Statistics Answer Key img_7\" width=\"300\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-9-Statistics-Answer-Key-img_7-300x110.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-9-Statistics-Answer-Key-img_7.png 645w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 7.<br \/>\nFind the numbers of faces, edges, and vertices of the solid.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24208\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.5-10.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 10\" width=\"175\" height=\"140\" \/><br \/>\nAnswer:<br \/>\nThe name of the solid is a pentagon.<br \/>\nNumber of vertices = 5<br \/>\nNumber of faces = 5<br \/>\nNumver of edges = 5<\/p>\n<p><strong>Write the word sentence as an equation.<\/strong><br \/>\nQuestion 8.<br \/>\n17 plus a number q is 40.<br \/>\nAnswer:<br \/>\nWe have to write the equation for the word sentence.<br \/>\nThe phrase &#8216;plus&#8217; indicates &#8216;+&#8217;<br \/>\n17 + q = 40<\/p>\n<p>Question 9.<br \/>\nThe product of a number s and 14 is 49.<br \/>\nAnswer:<br \/>\nWe have to write the equation for the word sentence.<br \/>\nThe phrase product indicates &#8216;\u00d7&#8217;<br \/>\ns \u00d7 14 = 49<\/p>\n<p>Question 10.<br \/>\nThe difference of a number b and 9 is 32.<br \/>\nAnswer:<br \/>\nWe have to write the equation for the word sentence.<br \/>\nThe phrase difference indicates &#8216;-&#8216;<br \/>\nb &#8211; 9 = 32<\/p>\n<p>Question 11.<br \/>\nThe quotient of 36 and a number g is 9.<br \/>\nAnswer:<br \/>\nWe have to write the equation for the word sentence.<br \/>\nThe phrase quotient indicates &#8216;\u00f7&#8217;<br \/>\n36 \u00f7 g = 9<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>FINDING DISTANCES FROM THE MEAN<\/strong> Find the average distance of each data value in the set from the mean. (See Exploration 1, p. 439.)<br \/>\nQuestion 12.<br \/>\nModel years of used cars on a lot: 2014, 2006, 2009, 2011, 2005<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nPrices of kites at a shop: $7, $20, $9, $35, $12, $15, $7, $10, $20, $25<br \/>\nAnswer:<\/p>\n<p><strong>FINDING THE MEAN ABSOLUTE DEVIATION<\/strong> Find and interpret the mean absolute deviation of the data.<br \/>\nQuestion 14.<br \/>\n69, 51, 71, 77, 71, 80, 75, 63, 73<br \/>\nAnswer:<br \/>\nGiven the data<br \/>\n69, 51, 71, 77, 71, 80, 75, 63, 73<br \/>\nNumber of samples = 9<br \/>\nMean Absolute Deviation = 70<\/p>\n<p>Question 15.<br \/>\n94, 86, 95, 99, 88, 90<br \/>\nAnswer:<br \/>\nGiven the data<br \/>\n94, 86, 95, 99, 88, 90<br \/>\nNumber of samples = 6<br \/>\nMean Absolute Deviation = 92<\/p>\n<p>Question 16.<br \/>\n46, 54, 43, 57, 50, 62, 78, 42<br \/>\nAnswer:<br \/>\nGiven the data<br \/>\n46, 54, 43, 57, 50, 62, 78, 42<br \/>\nNumber of samples = 8<br \/>\nMean Absolute Deviation = 54<\/p>\n<p>Question 17.<br \/>\n25, 28, 20, 22, 32, 28, 35, 34, 30, 36<br \/>\nAnswer:<br \/>\nGiven the data<br \/>\n25, 28, 20, 22, 32, 28, 35, 34, 30, 36<br \/>\nNumber of samples = 10<br \/>\nMean Absolute Deviation = 29<\/p>\n<p>Question 18.<br \/>\n101, 115, 124, 125, 173, 165, 170<br \/>\nAnswer:<br \/>\nGiven the data<br \/>\n101, 115, 124, 125, 173, 165, 170<br \/>\nNumber of samples = 7<br \/>\nMean Absolute Deviation = 139<\/p>\n<p>Question 19.<br \/>\n1.1, 7.5, 4.9, 0.4, 2.2, 3.3, 5.1<br \/>\nAnswer:<br \/>\nGiven the data<br \/>\n1.1, 7.5, 4.9, 0.4, 2.2, 3.3, 5.1<br \/>\nNumber of samples = 7<br \/>\nMean Absolute Deviation = 3.5<\/p>\n<p>Question 20.<br \/>\n\\(\\frac{1}{4}, \\frac{5}{8}, \\frac{3}{8}, \\frac{3}{4}, \\frac{1}{2}\\)<br \/>\nAnswer:<br \/>\nNumber of observations:5<br \/>\nMean (x\u0304): 0.5<br \/>\nMean Absolute Deviation (MAD): 0.15<\/p>\n<p>Question 21.<br \/>\n4.6, 8.5, 7.2, 6.6, 5.1, 6.2, 8.1, 10.3<br \/>\nAnswer:<br \/>\nNumber of observations:8<br \/>\nMean (x\u0304): 7.075<br \/>\nMean Absolute Deviation (MAD): 1.45<\/p>\n<p>Question 22.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend finds and interprets the mean absolute deviation of the data set 35, 40, 38, 32, 42, and 41. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24209\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.5-11.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 11\" width=\"305\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.5-11.png 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.5-11-300x161.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><br \/>\nAnswer:<br \/>\nx\u0304 = \u2211x\/n = (35 + 40 + 38)\/3<br \/>\n= 113\/3<br \/>\n= 37.6<br \/>\nYes, the data values are different from the mean by an average of 3.<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe data set shows the admission prices at several glass-blowing workshops.<br \/>\n$20, $20, $16, $12, $15, $25, $11<br \/>\nFind and interpret the range, interquartile range, and mean absolute deviation of the data.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24210\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.5-12.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 12\" width=\"252\" height=\"154\" \/><br \/>\nAnswer:<br \/>\nRange = (25 &#8211; 11)<br \/>\n= 14\/2<br \/>\n= 7<br \/>\nInterquartile range:<br \/>\nSamples = 7<br \/>\nXl = 12<br \/>\nXu = 20<br \/>\nXu &#8211; Xl = 20 &#8211; 12<br \/>\n= 8<br \/>\nAbsolute Deviation of the data:<br \/>\nData = 7<br \/>\nMean = 17<br \/>\nMean Absolute Deviation = 4<\/p>\n<p>Question 24.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe table shows the prices of the five most-expensive and least-expensive dishes on a menu. Find the MAD of each data set. Then compare their variations.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24211\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.5-13.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 13\" width=\"405\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.5-13.png 405w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.5-13-300x52.png 300w\" sizes=\"(max-width: 405px) 100vw, 405px\" \/><br \/>\nAnswer:<br \/>\nFive expensive dishes<br \/>\n$28, $30, $28, $39, $25<br \/>\nMAD:<br \/>\nDishes = 5<br \/>\nMean $30<br \/>\nMAD = $3.6<br \/>\nFirst leasr expensive dishes:<br \/>\n$7, $7, $10, $8, $12<br \/>\nMAD:<br \/>\nDishes = 5<br \/>\nMean $8.8<br \/>\nMAD = $1.76<br \/>\nMean Absolute Deviation of five most expensive dishes is greater than Mean Absolute Deviation of five least expensive dishes.<\/p>\n<p>Question 25.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe data sets show the years of the coins in two collections.<br \/>\nYour collection: 1950, 1952, 1908, 1902, 1955, 1954, 1901, 1910<br \/>\nYour friend\u2019s collection: 1929, 1935, 1928, 1930, 1925, 1932, 1933, 1920<br \/>\nCompare the measures of center and the measures of variation for each data set. What can you conclude?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24212\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.5-14.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 14\" width=\"132\" height=\"130\" \/><br \/>\nAnswer:<br \/>\nThe measure of center is a value of the center or middle of a data set.<br \/>\nThere are 4 measures of center they are<br \/>\nMean<br \/>\nMedian<br \/>\nMode<br \/>\nMidrange<br \/>\nfour measures of variations<br \/>\nRange<br \/>\nInterquartile range<br \/>\nVariance<br \/>\nStandard deviation<br \/>\nyour collection:<br \/>\nMean: (1950 + 1952 + 1908 + 1902 + 1955 + 1954 + 1901 + 1910)\/8<br \/>\n= 1,929<br \/>\nMedian: 1901, 1902, 1908, 1910, 1950, 1952, 1954, 1955<br \/>\n= (1910 + 1952)\/2<br \/>\n= 1930<br \/>\nMode: There is no mode<br \/>\nMidrange:<br \/>\n(1955 + 1901)\/2<br \/>\n= 3856\/2<br \/>\n= 1928<br \/>\nRange:<br \/>\n(1955 &#8211; 1901)\/2<br \/>\n= 54\/2<br \/>\n= 27<br \/>\nInterquartile range:<br \/>\nNumber of observations = 8<br \/>\nXl = 1903.5<br \/>\nXu = 1953.5<br \/>\nInterquartile range = 50<br \/>\nVariance = 655.14<br \/>\nStandard deviation = 25.59<\/p>\n<p>Question 26.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou survey students in your class about the numbers of movies they watched last month. A new student joins the class who watched 22 movies last month. Is22 an outlier? How does including this value affect the measures of center and the measures of variation? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24213\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-9-Statistical-Measures-9.5-15.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 9 Statistical Measures 9.5 15\" width=\"184\" height=\"149\" \/><br \/>\nAnswer:<\/p>\n<p><strong>REASONING<\/strong><br \/>\nWhich data set would have the greater mean absolute deviation? Explain your reasoning.<br \/>\nQuestion 27.<br \/>\nguesses for number of gumballs in a jar<br \/>\nguesses for number of baseballs in a jar<br \/>\nAnswer:<br \/>\nGumballs in the jar have a greater mean absolute deviation because baseballs are larger than baseballs.<\/p>\n<p>Question 28.<br \/>\nmonthly rainfall amounts in a city<br \/>\nmonthly amounts of water used in a home<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>REASONING<\/strong><br \/>\nRange, interquartile range, and mean absolute deviation are all measures of variation. Which measure of variation is most reliable? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 30.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nAdd and subtract the MAD from the mean in the original data set in Exercise 26.<br \/>\na. What percent of the values are within one MAD of the mean? two MADs of the mean? Which values are more than twice the MAD from the mean?<br \/>\nb. What do you notice as you get more and more MADs away from the mean? Explain.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Statistical_Measures_Connecting_Concepts\"><\/a>Statistical Measures Connecting Concepts<\/h3>\n<p><strong>Using the Problem-Solving Plan<\/strong><\/p>\n<p>Question 1.<br \/>\nSix friends play a carnival game in which a person throws darts at balloons. Each person throws the same number of darts and then records the portion of the balloons that pop. Find and interpret the mean, median, and MAD of the data.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24215\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-cc-1.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures cc 1\" width=\"278\" height=\"226\" \/><br \/>\nUnderstand the problem.<br \/>\nYou know that each person throws the same number of darts. You are given the portion of balloons popped by each person as a fraction, a decimal, or a percent.<\/p>\n<p>Make a plan.<br \/>\nFirst, write each fraction and each decimal as a percent. Next, order the percents from least to greatest. Then find and interpret the mean, median, and MAD of the data.<\/p>\n<p>Solve and check.<br \/>\nUse the plan to solve the problem. Then check your solution.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nThe cost c (in dollars) to rent skis at a resort for n days is represented by the equation c = 22n. The durations of several ski rentals are shown in the table. Find the range and interquartile range of the costs of the ski rentals. Then determine whether any of the costs are outliers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24216\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-cc-2.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures cc 2\" width=\"396\" height=\"100\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-cc-2.png 396w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-cc-2-300x76.png 300w\" sizes=\"(max-width: 396px) 100vw, 396px\" \/><br \/>\nAnswer:<br \/>\nGiven the equation c = 22n<br \/>\nc = 22(1) = 22<br \/>\nc = 22(5) = 1100<br \/>\nc = 22(1) = 22<br \/>\nc = 22(3) = 66<br \/>\nc = 22(5) = 110<br \/>\nc = 22(4) = 88<br \/>\nc = 22(3) = 66<br \/>\nc = 22(12) = 264<br \/>\nc = 22(1) = 22<br \/>\nc = 22(12) = 264<br \/>\nc = 22(5) = 110<br \/>\nc = 22(7) = 154<br \/>\nc = 22(4) = 88<br \/>\nc = 22(1) = 22<br \/>\n22, 110, 22, 66, 110, 88, 66, 264, 22, 264, 110, 154, 88, 22<br \/>\nRange = (264 &#8211; 22)\/2 = 242\/2<br \/>\n= 141<br \/>\nInterquartile range:<br \/>\nNumber of observations: 14<br \/>\nlower quartile = 22<br \/>\nupper quartile = 121<br \/>\nInterquartile range = upper quartile &#8211; lower quartile<br \/>\n= 121 &#8211; 22<br \/>\n= 99<\/p>\n<p><strong>Performance Task<\/strong><br \/>\nWhich Measure of Center Is Best: Mean, Median, or Mode?<br \/>\nAt the beginning of this chapter, you watched a STEAM Video called \u201cDaylight in the Big City.\u201c 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-24217\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-cc-3.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures cc 3\" width=\"400\" height=\"180\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-cc-3.png 400w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-cc-3-300x135.png 300w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<h3><a id=\"Statistical_Measures_Chapter_Review\"><\/a>Statistical Measures Chapter Review<\/h3>\n<p><strong>Review Vocabulary<\/strong><\/p>\n<p>Write the definition and give an example of each vocabulary term.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24218\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-cr-1.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures cr 1\" width=\"559\" height=\"104\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-cr-1.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-cr-1-300x56.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p><strong>Graphic Organizers<\/strong><\/p>\n<p>You can use a Definition and Example Chart to organize information about a concept. Here is an example of a Definition and Example Chart for the vocabulary term statistical question.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24219\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-cr-2.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures cr 2\" width=\"406\" height=\"283\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-cr-2.png 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-cr-2-300x209.png 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><\/p>\n<p>Choose and complete a graphic organizer to help you study the concept.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24220\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-cr-3.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures cr 3\" width=\"240\" height=\"340\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-cr-3.png 240w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-cr-3-212x300.png 212w\" sizes=\"(max-width: 240px) 100vw, 240px\" \/><br \/>\n1. mean<br \/>\n2. outlier<br \/>\n3. median<br \/>\n4. mode<br \/>\n5. range<br \/>\n6. quartiles<br \/>\n7. interquartile range<\/p>\n<p><strong>Chapter Self-Assessment<\/strong><\/p>\n<p>As 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-24221\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-crr-1.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 1\" width=\"590\" height=\"82\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-crr-1.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-crr-1-300x42.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p><strong>9.1 Introduction to Statistics (pp. 413\u2013418)<\/strong><br \/>\nLearning Target: Identify statistical questions and use data to answer statistical questions.<\/p>\n<p>Determine whether the question is a statistical question. Explain.<br \/>\nQuestion 1.<br \/>\nHow many positive integers are less than 20?<br \/>\nAnswer: There are only 19 numbers in that group<\/p>\n<p>Question 2.<br \/>\nIn what month were the students in a sixth-grade class born?<br \/>\nAnswer: February<\/p>\n<p>Question 3.<br \/>\nThe dot plot shows the number of televisions owned by each family on a city block.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24222\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-crr-3.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 3\" width=\"274\" height=\"96\" \/><br \/>\na. Find and interpret the number of data values on the dot plot.<br \/>\nb. Write a statistical question that you can answer using the dot plot. Then answer the question.<br \/>\nAnswer:<\/p>\n<p><strong>Display the data in a dot plot. Identify any clusters, peaks, or gaps in the data<\/strong><br \/>\nQuestion 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24223\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-crr-4.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 4\" width=\"201\" height=\"123\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24224\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-crr-5.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 5\" width=\"244\" height=\"121\" \/><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nYou conduct a survey to answer, \u201cWhat is the heart rate of a typical sixth-grade student?\u201d \ue033e table shows the results. Use the distribution of the data to answer the question.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24225\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-crr-6.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 6\" width=\"249\" height=\"179\" \/><br \/>\nAnswer:<\/p>\n<p><strong>9.2 Mean (pp. 419\u2013424)<\/strong><br \/>\nLearning Target: Find and interpret the mean of a data set.<\/p>\n<p>Question 7.<br \/>\nFind the mean of the data.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24226\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-crr-7.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 7\" width=\"537\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-crr-7.png 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-crr-7-300x33.png 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><br \/>\nAnswer:<br \/>\nx\u0304 = \u2211x\/n =(1112+1409+675+536+1398+162)\/6<br \/>\nx\u0304 = \u2211x\/n=6751\/6<br \/>\nx\u0304 = \u2211x\/n=1125.16<\/p>\n<p>Question 8.<br \/>\nThe double bar graph shows the monthly profit for two toy companies over a four-month period. Compare the mean monthly profits.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24227\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-crr-8.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 8\" width=\"299\" height=\"184\" \/><br \/>\nAnswer:<br \/>\nCompany A:<br \/>\n3.6, 3, 3.4, 4<br \/>\nMean: (3.6 + 3 + 3.4 + 4)\/4 = 14\/4 = 3.5<br \/>\nCompany B:<br \/>\n3, 4.3, 2.2, 4.1<br \/>\nMean: (3 + 4.3 + 2.2 + 4.1)\/4<br \/>\n= 13.6\/4<br \/>\n= 3.4<\/p>\n<p>Question 9.<br \/>\nThe table shows the test scores for a class of sixth-grade students. Describe how the outlier affects the mean. Then use the data to answer the statistical question, \u201cWhat is the typical test score for a student in the class?\u201d<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24228\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-crr-9.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 9\" width=\"152\" height=\"130\" \/><br \/>\nAnswer:<\/p>\n<p><strong>9.3 Measures of Center (pp. 425\u2013432)<\/strong><br \/>\nLearning Target: Find and interpret the median and mode of a data set.<\/p>\n<p><strong>Find the median and mode of the data.<\/strong><br \/>\nQuestion 10.<br \/>\n8, 8, 6, 8, 4, 5, 6<br \/>\nAnswer:<br \/>\nMedian:<br \/>\nwrite the given data in ascending order or descending order.<br \/>\n4, 5, 6, 8, 8, 8<br \/>\n= (6 + 8)\/2<br \/>\n= 14\/2<br \/>\n= 7<br \/>\nMode:<br \/>\n8 is the mode.<\/p>\n<p>Question 11.<br \/>\n24, 74, 61, 29, 38, 27, 68, 54<br \/>\nAnswer:<br \/>\nMedian:<br \/>\nwrite the given data in ascending order or descending order.<br \/>\n24, 74, 61, 29, 38, 27, 68, 54<br \/>\n= 24, 27, 29, 38, 54, 61, 68, 74<br \/>\n= (38 + 54)\/2<br \/>\n= 92\/2<br \/>\n= 48<br \/>\nMode:<br \/>\nThere is no mode in the data.<\/p>\n<p>Question 12.<br \/>\nFind the mean, median, and mode of the data set 67, 52, 50, 99, 66, 50, and 57 with and without the outlier. Which measure does the outlier affect the most?<br \/>\nAnswer:<br \/>\nGiven the data,<br \/>\n67, 52, 50, 99, 66, 50, and 57<br \/>\nMean with outliner:<br \/>\n(67 + 52 + 50 + 99 + 66 + 50 + 57)\/7<br \/>\n= 441\/7<br \/>\n= 63<br \/>\nMean without outliner:<br \/>\n66 is the median<br \/>\nMode with outliner: 50<br \/>\nMode without outliner:<br \/>\nNo mode<br \/>\nOutliners affect the mean value of the data but have little effect on the median or mode of a given set of data.<\/p>\n<p>Question 13.<br \/>\nThe table shows the lengths of several movies. Which measure of center best represents the data? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24229\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-crr-13.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 13\" width=\"152\" height=\"131\" \/><br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nGive an example of a data set that does not have a median. Explain why the data set does not have a median.<br \/>\nAnswer:<\/p>\n<p><strong>9.4 Measures of Variation (pp. 433\u2013438)<\/strong><br \/>\nLearning Target: Find and interpret the range and interquartile range of a data set.<\/p>\n<p><strong>Find the range of the data.<\/strong><br \/>\nQuestion 15.<br \/>\n45, 76, 98, 21, 52, 39<br \/>\nAnswer:<br \/>\nLowest value = 21<br \/>\nHighest value = 98<br \/>\nRange = (98 &#8211; 21)\/2<br \/>\n= 77\/2<br \/>\n= 38.5<\/p>\n<p>Question 16.<br \/>\n95, 63, 52, 8, 93, 16, 42, 37, 62<br \/>\nAnswer:<br \/>\nLowest value = 8<br \/>\nHighest value = 95<br \/>\nRange = (95 &#8211; 8)\/2<br \/>\n= 87\/2<br \/>\n= 43.5<\/p>\n<p><strong>Find the interquartile range of the data.<\/strong><br \/>\nQuestion 17.<br \/>\n28, 46, 25, 76, 18, 25, 47, 83, 44<br \/>\nAnswer:<br \/>\nGiven the data<br \/>\n28, 46, 25, 76, 18, 25, 47, 83, 44<br \/>\nNumber of observations: 9<br \/>\nlower quartile: 25<br \/>\nupper quartile: 61.5<br \/>\nInterquartile range (Xu &#8211; Xl) = 36.5<\/p>\n<p>Question 18.<br \/>\n14, 25, 97, 55, 66, 28, 92, 38, 94<br \/>\nAnswer:<br \/>\nGiven the data<br \/>\n14, 25, 97, 55, 66, 28, 92, 38, 94<br \/>\nNumber of observations: 9<br \/>\nlower quartile: 26.5<br \/>\nupper quartile: 93<br \/>\nInterquartile range (Xu &#8211; Xl) = 66.5<\/p>\n<p>Question 19.<br \/>\nThe table shows the weights of several adult emperor penguins. Find and interpret the range and interquartile range of the data. Then determine whether there are any outliers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24230\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-crr-19.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 19\" width=\"157\" height=\"160\" \/><br \/>\nAnswer:<br \/>\n25, 27, 36, 23.5, 33.5, 31.25, 30.75, 32, 24, 29.25<br \/>\nYes there are outliner<br \/>\nRange: (36\u00a0 &#8211; 25)\/2<br \/>\n= 11\/2<br \/>\n= 5.5<br \/>\nInterquartile range:<br \/>\nNumber of observations = 10<br \/>\nMean = 29.225<br \/>\nMAD = 3.98<\/p>\n<p>Question 20.<br \/>\nTwo data sets have the same interquartile range. Can you assume that the ranges of the two data sets are about the same? Give an example to justify your answer.<br \/>\nAnswer:<br \/>\n23<br \/>\nYes, a data set with the least value of 2 and the greatest value of 20 will have the same range as a data set with the least value of 82 and the greatest value of 100 will have the same range of 18.<\/p>\n<p><strong>9.5 Mean Absolute Deviation (pp. 439\u2013444)<\/strong><br \/>\nLearning Target: Find and interpret the mean absolute deviation of a data set.<\/p>\n<p><strong>Find and interpret the mean absolute deviation of the data.<\/strong><br \/>\nQuestion 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24231\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-crr-21.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 21\" width=\"169\" height=\"82\" \/><br \/>\nAnswer:<br \/>\nGiven data,<br \/>\n6, 8.5, 6, 9, 10, 7, 8, 9.5<br \/>\nNo. of observations: 8<br \/>\nMean = 8<br \/>\nMean Absolute Deviation: 1.25<\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24232\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-crr-22.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 22\" width=\"208\" height=\"88\" \/><br \/>\nAnswer:<br \/>\nGiven data,<br \/>\n130, 150, 190, 100, 175, 120, 165, 140, 180, 190<br \/>\nNo. of observations: 10<br \/>\nMean = 154<br \/>\nMean Absolute Deviation: 26<\/p>\n<p>Question 23.<br \/>\nThe table shows the prices of the five most-expensive and least-expensive manicures given by a salon technician on a particular day. Find the MAD of each data set. Then compare their variations.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24233\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-crr-23.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 23\" width=\"457\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-crr-23.png 457w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-crr-23-300x43.png 300w\" sizes=\"(max-width: 457px) 100vw, 457px\" \/><br \/>\nAnswer:<br \/>\nfive most-expensive:<br \/>\n$58, $52, $70, $49, $56<br \/>\nNo. of observations: 5<br \/>\nMean = 57<br \/>\nMean Absolute Deviation: 5.6<br \/>\n5 least-expensive manicures:<br \/>\n$10, $10, $15, $10, $15<br \/>\nNo. of observations: 5<br \/>\nMean = 12<br \/>\nMean Absolute Deviation: 2.4<br \/>\nThe Mean Absolute Deviation of the five most-expensive is greater than the Mean Absolute Deviation of the 5 least-expensive manicures.<\/p>\n<p>Question 24.<br \/>\nYou record the lengths of songs you stream. The next song is 276 seconds long. Is 276 an outlier? How does including this value affect the measures of center and the measures of variation? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24234\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-9-Statistical-Measures-crr-24.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 9 Statistical Measures crr 24\" width=\"253\" height=\"109\" \/><br \/>\nAnswer:<br \/>\nGiven the data,<br \/>\n233, 219, 163, 213, 224, 208, 225, 220, 222, 240, 228, 219, 260, 249, 209, 236,\u00a0 206<br \/>\nThe next song is 276 seconds long.<br \/>\n276 is the outliner.<br \/>\nWe can remove 276 from the given data set.<br \/>\nSo, there is no effect on the center and the measure of variations.<\/p>\n<h3><a id=\"Statistical_Measures_Practice_Test\"><\/a>Statistical Measures Practice Test<\/h3>\n<p><strong>Find the mean, median, mode, range, and interquartile range of the data.<\/strong><br \/>\nQuestion 1.<br \/>\n5, 6, 4, 24, 10, 6, 9, 8<br \/>\nAnswer:<br \/>\nMean = (5 + 6 + 4 + 24 + 10 + 6 + 9 + 8)\/8<br \/>\n= 72\/8<br \/>\n= 9<br \/>\nMedian:<br \/>\n4, 5, 6, 6, 8, 9, 10, 24<br \/>\n= (6 + 8)\/2 = 14\/2<br \/>\n= 7<br \/>\nMode:<br \/>\n6 is the mode<br \/>\nrange = (24 &#8211; 4)\/2<br \/>\n= 20\/2<br \/>\n= 10<br \/>\nRange:<br \/>\nLowest value: 4<br \/>\nHighest value: 24<br \/>\nRange: 20<br \/>\nInterquartile range:<br \/>\nLower quartile (xL): 5.25<br \/>\nUpper quartile (xU): 9.75<br \/>\nInterquartile range (xU-xL): 4.5<\/p>\n<p>Question 2.<br \/>\n46, 27, 94, 56, 53, 65, 43<br \/>\nAnswer:<br \/>\nGiven the data,<br \/>\n46, 27, 94, 56, 53, 65, 43<br \/>\nMean = (46 + 27 + 94 + 56 + 53 + 65 + 43)\/7<br \/>\n= 16.75<br \/>\nMedian = 15.5<br \/>\nMode: There is no mode<br \/>\nRange:<br \/>\nNumber of observations = 7<br \/>\nLowest value: 27<br \/>\nHighest value: 94<br \/>\nRange: 67<br \/>\nInterquartile range:<br \/>\nLower quartile (xL): 43<br \/>\nUpper quartile (xU): 65<br \/>\nInterquartile range (xU-xL): 22<\/p>\n<p>Question 3.<br \/>\n32, 58, 19, 36, 44, 57, 11, 26, 74<br \/>\nAnswer:<br \/>\nGiven the data,<br \/>\n32, 58, 19, 36, 44, 57, 11, 26, 74<br \/>\nMean = (32 + 58 + 19 + 36 + 44 + 57 + 11 + 26 + 74)\/9<br \/>\n= 357\/9<br \/>\n= 39.66<br \/>\nMedian:<br \/>\nArrange the data in ascending or descending order.<br \/>\n11, 19, 26, 32, 36, 44, 57, 58, 74<br \/>\nMedian = 36<br \/>\nMode: There is no mode in the data<br \/>\nRange:<br \/>\nLowest value: 11<br \/>\nHighest value: 74<br \/>\nRange: 63<br \/>\nInterquartile range:<br \/>\nLower quartile (xL): 22.5<br \/>\nUpper quartile (xU): 57.5<br \/>\nInterquartile range (xU-xL): 35<\/p>\n<p>Question 4.<br \/>\n36, 24, 49, 32, 37, 28, 38, 40, 39<br \/>\nAnswer:<br \/>\nGiven the data<br \/>\n36, 24, 49, 32, 37, 28, 38, 40, 39<br \/>\nArrange the data in ascending or descending order.<br \/>\n24, 28, 32, 36, 37, 38, 39, 40, 49<br \/>\nMean = (24 + 28 + 32 + 36 + 37 + 28 + 38 + 40 + 49)\/9<br \/>\n= 34.66<br \/>\nMedian: 37<br \/>\nMode: There is no mode<br \/>\nRange:<br \/>\nLowest value: 24<br \/>\nHighest value: 49<br \/>\nRange: 25<br \/>\nInterquartile range:<br \/>\nLower quartile (xL): 30<br \/>\nUpper quartile (xU): 39.5<br \/>\nInterquartile range (xU-xL): 9.5<\/p>\n<p><strong>Find and interpret the mean absolute deviation of the data.<\/strong><br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24243\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-pt-5.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures pt 5\" width=\"206\" height=\"88\" \/><br \/>\nAnswer:<br \/>\nGiven the data,<br \/>\n312, 286, 196, 201, 158, 225, 206, 192<br \/>\nMean (x\u0304): 0.5<br \/>\nMean Absolute Deviation (MAD): 0.15<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-pt-6.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures pt 6\" width=\"252\" height=\"86\" \/><br \/>\nAnswer:<br \/>\nGiven the data,<br \/>\n15, 8, 19, 20, 18, 20, 22, 14, 10, 15<br \/>\nMean (x\u0304): 16.1<br \/>\nMean Absolute Deviation (MAD): 3.7<\/p>\n<p>Question 7.<br \/>\nYou conduct a survey to answer, \u201cHow many Times (minutes)minutes does it take a typical sixth-grade student to run a mile?\u201d The table shows the results. Use the distribution of the data to answer the question.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24245\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-pt-7.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures pt 7\" width=\"208\" height=\"113\" \/><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nThe table shows the weights of Alaskan malamute 8181808281dogs at a veterinarian\u2019s office. Which measure of center best represents the weight of an Alaskan malamute? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24246\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-pt-8.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures pt 8\" width=\"250\" height=\"104\" \/><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nThe table shows the numbers of guests Numbers of Guests at a hotel on different days.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24247\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-pt-9.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures pt 9\" width=\"239\" height=\"88\" \/><br \/>\na. Find the range and interquartile range of the data.<br \/>\nb. Use the interquartile range to identify the outlier(s) in the data set. Find the range and interquartile range of the data set without the outlier(s). Which measure did the outlier or outliers affect more?<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nThe data sets show the numbers of hours worked each week by two people for several weeks.<br \/>\nPerson A: 9, 18, 12, 6, 9, 21, 3, 12<br \/>\nPerson B: 12, 18, 15, 16, 14, 12, 15, 18<br \/>\nCompare the measures of center and the measures of variation for each data set. What can you conclude?<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nThe table shows the lengths of several bearded dragons captured for a study. Find the mean, median, and mode of the data in centimeters and in inches. How does converting to inches affect the mean, median, and mode?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24248\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-pt-11.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures pt 11\" width=\"243\" height=\"227\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Statistical_Measures_Cumulative_Practice\"><\/a>Statistical Measures Cumulative Practice<\/h3>\n<p>Question 1.<br \/>\nWhich statement can be represented by a negative integer?<br \/>\nA. The temperature rises 15 degrees.<br \/>\nB. A hot-air balloon ascends 450 yards.<br \/>\nC. You earn $50 completing chores.<br \/>\nD. A submarine submerges 260 feet.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24235\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-cp-1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures cp 1\" width=\"301\" height=\"372\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-cp-1.png 301w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-cp-1-243x300.png 243w\" sizes=\"(max-width: 301px) 100vw, 301px\" \/><br \/>\nAnswer: D. A submarine submerges 260 feet.<\/p>\n<p>Question 2.<br \/>\nWhat is the height h (in inches) of the prism?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24236\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-cp-2.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures cp 2\" width=\"328\" height=\"173\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-cp-2.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-cp-2-300x158.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nAnswer:<br \/>\nh = v\/lw<br \/>\nh = 5850\/30(12 1\/4)<br \/>\nh = 5850\/(30 \u00d7 12.25)<br \/>\nh = 5850\/367.50<br \/>\nh = 15.91 inches<\/p>\n<p>Question 3.<br \/>\nWhich is the solution of the inequality \\(\\frac{2}{3}\\)x &lt; 6?<br \/>\nF. x &lt; 4<br \/>\nG. x &lt; 5\\(\\frac{1}{3}\\)<br \/>\nH. x &lt; 6\\(\\frac{2}{3}\\)<br \/>\nI. x &lt; 9<br \/>\nAnswer: I. x &lt; 9<\/p>\n<p>Question 4.<br \/>\nThe number of hours that each of six students spent reading last week is shown in the bar graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24237\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-cp-4.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures cp 4\" width=\"277\" height=\"189\" \/><br \/>\nFor the data in the bar graph, which measure is the?<br \/>\nA. mean<br \/>\nB. median<br \/>\nC. mode<br \/>\nD. range<br \/>\nAnswer: C. mode<\/p>\n<p>Explanation:<br \/>\nIn the above bar graph, 10 is repeated two ways.<br \/>\nThus the correct answer is option C.<\/p>\n<p>Question 5.<br \/>\nWhich list of numbers is in order from least to greatest?<br \/>\nF. &#8211; 5.41, &#8211; 3.6, &#8211; 3.2, &#8211; 3.06, &#8211; 1<br \/>\nG. &#8211; 1, &#8211; 3.06, &#8211; 3.2, &#8211; 3.6, &#8211; 5.41<br \/>\nH. &#8211; 5.41, &#8211; 3.06, &#8211; 3.2, &#8211; 3.6, &#8211; 1<br \/>\nI. &#8211; 1, &#8211; 3.6, &#8211; 3.2, &#8211; 3.06, &#8211; 5.41<br \/>\nAnswer: F. &#8211; 5.41, &#8211; 3.6, &#8211; 3.2, &#8211; 3.06, &#8211; 1<\/p>\n<p>Explanation:<br \/>\nWe have to write the numbers from least to greatest<br \/>\nThe negative sign with the highest number will be the least.<br \/>\n&#8211; 5.41, &#8211; 3.6, &#8211; 3.2, &#8211; 3.06, &#8211; 1<br \/>\nThus the correct answer is option F.<\/p>\n<p>Question 6.<br \/>\nWhat is the mean absolute deviation of the data shown in the dot plot, rounded to the nearest tenth?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24238\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-cp-6.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures cp 6\" width=\"232\" height=\"112\" \/><br \/>\nA. 1.4<br \/>\nB. 3<br \/>\nC. 3.2<br \/>\nD. 57.<br \/>\nAnswer:<br \/>\nData from the dot plot<br \/>\n5, 5, 4, 4, 6, 1<br \/>\nNumber of observations: 6<br \/>\nMean = 4.166<br \/>\nMean absolute deviation = 1.66<br \/>\nThus the correct answer is option A.<\/p>\n<p>Question 7.<br \/>\nA family wants to buy tickets to a theme park. There are separate ticket prices for adults and children.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24239\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-cp-7.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures cp 7\" width=\"281\" height=\"94\" \/><br \/>\nWhich expression represents the total cost (in dollars) for adult tickets c and child tickets?<br \/>\nF. 600 (a + c)<br \/>\nG. 50(a \u00d7 c)<br \/>\nH. 30a + 20c<br \/>\nI. 30a \u00d7 20c<br \/>\nAnswer: H. 30a + 20c<\/p>\n<p>Question 8.<br \/>\nThe dot plot shows the leap distances (in feet) of a tree frog. How many leaps were recorded?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24240\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-cp-8.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures cp 8\" width=\"532\" height=\"115\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-cp-8.png 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-cp-8-300x65.png 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><br \/>\nAnswer: 7 leaps were recorded<\/p>\n<p>Question 9.<br \/>\nWhat is the value of the expression when a = 6 and b = 14?<br \/>\n0.8a + 0.02b<br \/>\nA. 0.4828<br \/>\nB. 0.8814<br \/>\nC. 5.08<br \/>\nD. 16.4<br \/>\nAnswer:<br \/>\nGiven the expression,<br \/>\n0.8a + 0.02b<br \/>\na = 6<br \/>\nb = 14<br \/>\n0.8(6) + 0.02(14)<br \/>\n4.8 + 0.28<br \/>\n= 5.08<br \/>\nThus the correct answer is option C.<\/p>\n<p>Question 10.<br \/>\nWhich property was not used to simplify the expression?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24241\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-cp-10.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures cp 10\" width=\"290\" height=\"126\" \/><br \/>\nF. Distributive Property<br \/>\nG. Associative Property of Addition<br \/>\nH. Multiplication Property of One<br \/>\nI. Commutative Property of Multiplication<br \/>\nAnswer: I. Commutative Property of Multiplication<\/p>\n<p>Question 11.<br \/>\nWhat are the coordinates of Point P?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24242\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-9-Statistical-Measures-cp-11.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures cp 11\" width=\"174\" height=\"179\" \/><br \/>\nA. (- 3, &#8211; 2)<br \/>\nB. (3, &#8211; 2)<br \/>\nC. (- 2, &#8211; 3)<br \/>\nD. (-2, 3)<br \/>\nAnswer: B. (3, &#8211; 2)<\/p>\n<p>Explanation:<br \/>\nBy seeing the above graph we can write the ordered pair P.<br \/>\nthe x-axis is on 3 and the y-axis is on -2<br \/>\nThus the correct answer is option B.<\/p>\n<p>Question 12.<br \/>\nCreate a data set with 5 numbers that has the following measures.<br \/>\nThink<br \/>\nSolve<br \/>\nExplain<br \/>\n\u2022 a mean of 7<br \/>\n\u2022 a median of 9<br \/>\nExplain how you created your data set.<br \/>\nAnswer:<br \/>\nThe data set is 3, 2, 9, 1, 20<\/p>\n<p><em>Final Words:<\/em><\/p>\n<p>We hope that the article on Big Ideas Math Answers Grade 6 Chapter 9 Statistical Measures helps you in all over preparation. If you are lagging in this concept, then you can check the above material. Feel free to post your doubts or comments in the comments section. If you need solutions to any of the questions, then you can ask us in the comment section itself. We clear all your doubts as early as possible. 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