## Engage NY Eureka Math Grade 6 Module 6 Lesson 2 Answer Key

### Eureka Math Grade 6 Module 6 Lesson 2 Example Answer Key

Example 1: Heart Rate

Mia, a sixth-grader at Roosevelt Middle School, was thinking about joining the middle school track team. She read that Olympic athletes have lower resting heart rates than most people. She wondered about her own heart rate and how it would compare to other students. Mia was interested in investigating the statistical question: What are the heart rates of students in my sixth-grade class?

Heart rates are expressed as beats per minute (or bpm). Mia knew her resting heart rate was 80 beats per minute. She asked her teacher if she could collect the heart rates of the other students in her class. With the teacher’s help, the other sixth graders in her class found their heart rates and reported them to Mia. The following numbers are the resting heart rates (in beats per minute) for the 22 other students in Mia’s class.
89 87 85 84 90 79 83 85 86 88 84 81 88 85 83 83 86 82 83 86 82 84.

Exercises 1 – 10:

Exercise 1.
What was the heart rate for the student with the lowest heart rate?
79 bpm

Exercise 2.
What was the heart rate for the student with the highest heart rate?
90 bpm

Exercise 3.
How many students had a heart rate greater than 86 bpm?
5

Exercise 4.
What fraction of students had a heart rate less than 82 bpm?
$$\frac{2}{22}$$ or $$\frac{1}{11}$$

Exercise 5.
What heart rate occurred most often?
83 bpm

Exercise 6.
What heart rate describes the center of the data?
85 bpm (Answers will vary, but student responses should be around 84 bpm or 85 bpm.)

Exercise 7.
Some students had heart rates that were unusual in that they were quite a bit higher or quite a bit lower than most other students’ heart rates. What heart rates would you consider unusual?
Answers will vary and could include 79 bpm. 81 bpm. 87 bpm, 88 bpm,. 89 bpm. and/or 90 bpm.

Exercise 8.
If Mia’s teacher asked what the typical heart rate is for sixth graders in the class, what would you tell Mia’s teacher?
Answers will vary, but expect answers between 82 bpm and 86 bpm.

Exercise 9.
Remember that Mia’s heart rate was 80 bpm. Add a dot for Mia’s heart rate to the dot plot in Example 1.
Add o dot above 80 bpm on the number line.

Exercise 10.
How does Mia’s heart rate compare with the heart rates of the other students in the class?
Her heart rate ¡s lower than all but one of the students.

Example 2: Seeing the Spread in Dot Plots.

Mia’s class collected data to answer several other questions about her class. After collecting the data, they drew dot
plots of their findings. One student collected data to answer the question: How many textbooks are in the desks or lockers of sixth graders? She made the following dot plot, not including her data.

Dot Plot of Number of Textbooks

Another student in Mia’s class wanted to ask the question: How tall are the sixth graders in our class?
This dot plot shows the heights of the sixth graders in Mia’s class, not including the datum for the student conducting the
survey.
Dot Plot of Height

Exercises 11 – 14:

Below are four statistical questions and four different dot plots of data collected to answer these questions. Match each statistical question with the appropriate dot plot, and explain each choice.

Statistical Questions:

Exercise 11.
What are the ages of fourth-graders in our school?
Dot plot A because most fourth-graders are around 9 or 10 years old.

Exercise 12.
What are the heights of the players on the eighth-grade boys’ basketball team?
Dot plot D because the players on an eighth-grade basketball team can vary in height. Generally, there ¡s a tall
player (73 inches), while most others are between 5 feet, or 60 inches, and 5 feet 4 inches, or 64 inches.

Exercise 13.
How many hours of W do sixth graders in our class watch on a school night?
Dot plot B; explanations will vary. For example, a student might say, “I think a few of the students may watch a lot
of W. Most students watch two hours or less.”

Exercise 14.
How many different languages do students ¡n our class speak?

Dot plot C because most students know one language, English. Many students in our class also study another language or live in an environment where their families speak another language.

### Eureka Math Grade 6 Module 6 Lesson 2 Problem Set Answer Key

Question 1.
The dot plot below shows the vertical jump height (in inches) of some NBA players. A vertical jump height is how high a player can jump from a standstill.

Dot Plot of Vertical Jump

a. What statistical question do you think could be answered using these data?
What are the vertical jump heights of NBA players?

b. What was the highest vertical jump by a player?
43 inches

c. What was the lowest vertical jump by a player?
32 inches

d. What is the most common vertical jump height (the height that occurred most often)?
38 inches

e. How many players jumped the most common vertical jump height?
10

f. How many players jumped higher than 40 inches?
3

g. Another NBA player jumped 33 inches. Add a dot for this player on the dot plot. How does this player compare with the other players?
Add another dot above 33. This player jumped the same os two other players and jumped higher than only
one player.

Question 2.
Below are two statistical questions and two different dot plots of data collected to answer these questions. Match each statistical question with its dot plot, and explain each choice.
Statistical Questions:

a. What is the number of fish (if any) that students in a class have in an aquarium at their homes?
A; some students may not have any fish (O from the dot plot), while another student has 10 fish.

b. How many days out of the week do the children on my street go to the playground?
Dot Plot A

Dot Plot B

B; the dot plot displays the values 2, 3, 4, 5, and 6, which are all reasonable within the context of the question.

Question 3.
Read each of the following statistical questions. Write a description of what the dot plot of the data collected to
answer the question might look like. Your description should include a description of the spread of the data and the center of the data.

a. What is the number of hours sixth graders are in school during a typical school day?
Most students are in school for the same number of hours, so the spread would be smalL Differences may exist for those students who might have doctor’s appointments or who participate in a club or an afterschool activity. Student responses vary based on their estimates of the number of hours students spend in schooL

b. What is the number of video games owned by the sixth graders in our class?
These data would have a very big spread. Some students might have no video games, while others could have a large number of games. A typical value of 5 (or something similar) would identify a center. In this case, the center is based on the number most commonly reported by students.

### Eureka Math Grade 6 Module 6 Lesson 2 Exit Ticket Answer Key

A sixth-grade class collected data on the number of letters in the first names (name lengths) of all the students in class. Here is the dot plot of the data they collected:

Question 1.
How many students are in the class?
There are 25 students in the class.

Question 2.
What is the shortest name length?
The shortest name length is 3 letters.

Question 3.
What is the longest name length?