## Engage NY Eureka Math Grade 6 Module 6 Lesson 5 Answer Key

### Eureka Math Grade 6 Module 6 Lesson 5 Example Answer Key

Example 1: Relative Frequency Table

In Lesson 4, we investigated the head circumferences that the boys’ and girls’ basketball teams collected. Below is the frequency table of the head circumferences that they measured.

Isabel, one of the basketball players, indicated that most of the caps were small (S), medium (M), or large (L). To decide if Isabel was correct, the players added a relative frequency column to the table.

Relative frequency is the frequency for an interval divided by the total number of data values. For example, the relative frequency for the extra small (XS) cap is 2 divided by 40, or 0.05. This represents the fraction of the data values that were XS.

Exercises 1 – 4:

Exercise 1.
Complete the relative frequency column in the table below.

Exercise 2.
What is the total of the relative frequency column?
The total of the relative frequency column is 1.000, or 100%.

Exercise 3.
Which interval has the greatest relative frequency? What is the value?
The interval with the greatest relative frequency is the medium-sized caps, 550—569, which has a relative frequency of 0. 375, or 37. 5%.

Exercise 4.
What percentage of the head circumferences are between 530 and 589 mm? Show how you determined the
0.200 + 0.375 + 0.225 = 0.800, or 80%

Example 2: Relative Frequency Histogram

The players decided to construct a histogram using the relative frequencies instead of the frequencies. They noticed that the relative frequencies in the table ranged from close to 0 to about 0.40. They drew a number line and marked off the intervals on that line. Then, they drew the vertical line and labeled it Relative Frequency. They added a scale to this line by starting at 0 and counting by 0.05 until they reached 0.40.

They completed the histogram by drawing the bars so the height of each bar matched the relative frequency for that interval. Here is the completed relative frequency histogram:

Exercises 5 – 6:

Exercise 5.

a. Describe the shape of the relative frequency histogram of head circumferences from Example 2.
The shape of the relative frequency is slightly skewed to the right.

b. How does the shape of this relative frequency histogram compare with the frequency histogram you drew in Exercise 5 of Lesson 4?
The shape is the same in both histograms.

c. Isabel said that most of the caps that needed to be ordered were small (S), medium (M), and large (L). Was she right? What percentage of the caps to be ordered are small, medium, or large?
She was right. The total percentage of the small, medium and large cops was 80% (20% small, 37.5% medium, and 22. 5% large, for a total of 80%).

Exercise 6.
Here is the frequency table of the seating capacity of arenas for the NBA basketball teams.

a. What is the total number of NBA arenas?
There are 29 NBA arenas in total.

b. Complete the relative frequency column. Round the relative frequencies to the nearest thousandth.
See the table above.

c. Construct a relative frequency histogram.

d. Describe the shape of the relative frequency histogram.
The shape is slightly skewed to the right.

e. What percentage of the arenas have a seating capacity between 18, 500 and 19.999 seats?
Approximately 0.516, or 51.6%, of the arenas have a seating capacity between 18,500 and 19,999 seats.

f. How does this relative frequency histogram compare to the frequency histogram that you drew in Problem 2 of the Problem Set in Lesson 4?
Both histograms have the same shape.

### Eureka Math Grade 6 Module 6 Lesson 5 Problem Set Answer Key

Question 1.
Below is a relative frequency histogram of the maximum drop (in feet) of a selected group of roller coasters.

a. Describe the shape of the relative frequency histogram.
The shape is skewed to the right.

b. What does the shape tell you about the maximum drop (in feet) of roller coasters?
The shape tells us most of the roller coasters have o maximum drop that is between 50 and 170 feet but that some roller coasters have a maximum drop that is quite a bit larger than the others.

c. Jerome said that more than half of the data values are in the interval from 50 to 130 feet. Do you agree with Jerome? Why or why not?
I agree with Jerome because that interval contains 60% of the data.

Question 2.
The frequency table below shows the length of selected movies shown in a local theater over the past 6 months.

a. Complete the relative frequency column. Round the relative frequencies to the nearest thousandth.

b. What percentage of the movie lengths are greater than or equal to 130 minutes?
0.107 + 0.036 = 0. 143, or 14.3% of the movie lengths are greater than or equal to 130 minutes.

c. Draw a relative frequency histogram. (Hint: Label the relative frequency scale starting at O and going up to 0.30, marking off intervals of 0.05.)

d. Describe the shape of the relative frequency histogram.
The histogram is mound shaped and approximately symmetric.

e. What does the shape tell you about the length of movie times?
The shape tells us the length of most movies is between 100 and 130 minutes.

Question 3.
The table below shows the highway miles per gallon of different compact cars.

a. What is the total number of compact cars?
The total number of compact cars is 16.

b. Complete the relative frequency column. Round the relative frequencies to the nearest thousandth.

c. What percentage of the cars get between 31 and up to but not including 37 miles per gallon on the highway?
0.250 + 0.313 = 0.563, or 56.3% of the cars get between 31 and up to 37 miles per gallon on the highway.

d. Juan drew the relative frequency histogram of the highway miles per gallon for the compact cars, 0.35 shown on the right. Did Juan draw the histogram correctly? Explain your answer.

Juan did not draw the histogram correctly because he did not leave spaces far intervals 43-< 46 and 46-< 49. These spaces are needed to represent the relative frequency of zero. He also forgot to draw a bar for the final interval, 49-< 52.

### Eureka Math Grade 6 Module 6 Lesson 5 Exit Ticket Answer Key

Question 1.
Calculators are allowed for completing your problems.

Hector’s mom had a rummage sale, and after she sold an item, she tallied the amount of money she received for the item. The following is the frequency table Hector’s mom created:

a. What was the total number of items sold at the rummage sale?
c. What percentage of the items Hector’s mom sold were sold for $15 or more but less than$20?
37% of the items Hector’s mom sold were sold for $15 or more but less than$20.