We included **HMH Into Math Grade 6 Answer Key PDF** **Module 14 Lesson 2 Display Data in Dot Plots **to make students experts in learning maths.

## HMH Into Math Grade 6 Module 14 Lesson 2 Answer Key Display Data in Dot Plots

I Can construct and analyze a dot plot.

**Step It Out**

Statistical questions are answered by collecting and analyzing data. One way to understand a set of data is to make a visual display. A dot plot is a type of line plot that shows the frequency of each data value using a dot.

Connect to Vocabulary

A dot plot is a visual display in which each piece of data is represented by a dot above a number line. The number of times a data value occurs is called the frequency.

Question 1.

A pulse rate is the number of times a heart beats in a minute. The pulse rate for a group of 12-year-olds is taken before physical education class. The results are shown in the table. Which pulse rate is the most common among the group?

A. Complete the number line with an appropriate scale.

Pulse rates vary from to , so I should use a scale from to.

Answer: Pulse rates vary from 55 to 85, so I should use a scale from 55 to 85.

B. For each piece of data, plot a dot above the number that corresponds to that data value.

Answer:

C. Which pulse rate is the most common among the group of 12-year-olds? Explain how you know.

Answer: 75 is the most common among the group of 12-year-olds.

**Turn and Talk** Are dot plots useful for a large volume of data? Explain.

Answer: Dot plots help you visualize the shape and spread of sample data and are especially useful for comparing frequency distributions. Dot plots are one of the simplest statistical plots and are suitable for small to moderate-sized data sets.

Question 2.

A company’s employees are rated for their customer service on a scale of 1-10, with 1 being very unhappy and 10 being very happy with the service. The customer service ratings for one day are shown in the dot plot. Use the dot plot to describe the data.

A. What is the most common rating for the day? Explain how you know.

Answer: 7 is the most common rating for the day.

B. What is the least common rating for the day? Explain how you know.

Answer: 1 is the least common rating for the day.

C. How many observations are shown in the dot plot?

Answer: 40 observations are shown in the dot plot.

D. If a rating of 6 or higher is considered acceptable by the company, what percent of the ratings are unacceptable?

There are total ratings and ratings below 6. So, , or % of the ratings, are considered unacceptable by the company.

Answer: There are 40 total ratings and 12 ratings below 6. So, 12/40, or 30% of the ratings, are considered unacceptable by the company.

E. If a rating of greater than 8 is considered excellent, what percent of the ratings for the day are excellent?

There are total ratings and ratings greater than 8. So, , or of the ratings, are considered excellent.

Answer: There are 40 total ratings and 9 ratings greater than 8. So, 9/40, or 22.5% of the ratings, are considered excellent.

F. There are 5 additional customer ratings at the end of the day, each a rating of 10. Will this change your answers to Parts A-E? Explain.

Answer: Yes if 5 additional customer ratings at the end of the day, each a rating of 10 then the most common rating for the day will be changed from 7 to 9. The number of observations will be changed. The percentage of the ratings for the day are excellent will be changed.

**Turn and Talk** How is a dot plot different from a number line? Explain.

Answer:

Question 3.

The recommended amount of water that each person should drink per day is shown. Students are asked to track how much water they actually drink in a day. The number of glasses of water they drank on a specific day is shown in the following list.

5, 7, 9, 7, 6, 1, 4, 2, 3, 0, 8, 5, 2, 5, 6, 7, 4, 8, 5, 6, 4, 3, 8, 6, 5

A. Complete the dot plot to show the amount of water students drank per day.

Answer:

Given data,

5, 7, 9, 7, 6, 1, 4, 2, 3, 0, 8, 5, 2, 5, 6, 7, 4, 8, 5, 6, 4, 3, 8, 6, 5

B. What is the most common number of glasses of water students drank?

Answer: The most common number of glasses of water students drank is 5.

C. How many students drank at least the recommended amount of water per day?

Answer: 4 students drank at least the recommended amount of water per day.

D. How many observations are shown in the dot plot?

Answer: 25 observations are shown in the dot plot.

E. What percentage of students did not drink at least the recommended amount of water per day?

Answer: 4 percent of students did not drink at least the recommended amount of water per day.

**Check Understanding**

Question 1.

The shoe sizes of the players on a soccer team are shown in the list.

10.5, 11.5, 10, 9, 10.5, 10, 8, 9, 7.5, 8, 10.5, 11, 10, 10.5, 9.5, 8.5, 7, 8.5, 9, 9.5, 10, 10.5, 11

Complete the dot plot to show the shoe sizes of the players.

Answer:

Given data,

10.5, 11.5, 10, 9, 10.5, 10, 8, 9, 7.5, 8, 10.5, 11, 10, 10.5, 9.5, 8.5, 7, 8.5, 9, 9.5, 10, 10.5, 11

Question 2.

A student is asked to make a dot plot with the list shown.

8, 11, 16, 27, 8, 10, 19, 21, 7, 12, 15, 16, 22, 13

How many observations will be shown in the dot plot?

Answer: 14 observations will be shown in the dot plot.

**On Your Own**

Question 3.

**Attend to Precision** The dot plot shows the thicknesses of sheets of cardstock, a type of paper.

A. What is the least thickness measured?

Answer: 7 is the least thickness measured.

B. What is the greatest thickness measured?

Answer: 8 is the greatest thickness measured.

C. What is the most common thickness measured?

Answer: 7.7 is the most common thickness measured.

Question 4.

A group of people is asked to count the number of coins in their pockets or wallets. The number of coins each person has is shown in the list.

7, 10, 2, 0, 6, 8, 5, 3, 4, 0, 9, 1, 8, 7, 10, 0, 5, 7

A. Complete the dot plot for the number of coins each person had.

Answer:

B. What is the most common number of coins in a person’s pockets?

Answer: By seeing the above dot plot we can say that 7 is the most common number of coins in a person’s pockets

C. How many observations are shown in the dot plot?

Answer: By seeing the above dot plot we can say that there are 20 observations in the dot plot.

D. What percentage of people had more than 5 coins in their pockets?

Answer: 8 people more than 5 coins in their pockets.

40% of people had more than 5 coins in their pockets

E. What percentage of people had fewer than 7 coins in their pockets?

Answer: 10 people had fewer than 7 coins in their pockets.

50% of people had fewer than 7 coins in their pockets.

Question 5.

A basketball team tracks the number of three-point shots it makes per game during a season of games, as shown in the dot plot.

A. In how many games did the team score at least 3 three-point shots?

Answer: In 3 games the team score at least 3 three-point shots

B. In how many games did the team score exactly 9 points from three-point shots?

Answer: In 2 games the team scores exactly 9 points from three-point shots.

C. What is the most three-point shots made in a game?

Answer: 3 is the most three-point shots made in a game.

D. What percent of the games did the team score at least 3 three-point shots?

Answer:

Question 6.

The masses of a set of gemstones a jeweler has for jewelry are listed.

Gemstone masses (in grams): 0.2, 0.5, 0.1, 0.4, 0.7, 0.5, 0.3, 0.2, 0.1, 0.4, 0.2, 0.5, 0.2, 0.3, 0.1, 0.2, 0.6, 0.2, 0.6, 0.1

A. Make a dot plot to show the masses of the gemstones.

Answer:

Given data,

Gemstone masses (in grams): 0.2, 0.5, 0.1, 0.4, 0.7, 0.5, 0.3, 0.2, 0.1, 0.4, 0.2, 0.5, 0.2, 0.3, 0.1, 0.2, 0.6, 0.2, 0.6, 0.1

B. How many observations are shown in the dot plot?

Answer: 20 observations are shown in the dot plot.

C. What is the most common mass of gemstone?

Answer: 0.2 is the most common mass of gemstone.

D. Which gemstone mass is the least common?

Answer: 0.7 gemstone mass is the least common.

Question 7.

**Reason** The dot plot shows the numbers of pages students in a class read during their dedicated reading time.

A. How many students are in the class?

Answer: There are 20 students in the class.

B. What percent of students read more than 6 pages? Explain your reasoning.

Answer: 5 students read more than 6 pages

5/20 = 1/4 = 0.25

25 percent of students read more than 6 pages.

C. What fraction of the students read fewer than 5 pages?

Answer:

12/20 = 3/5 fraction of the students read fewer than 5 pages.

D. How many total pages did all of the students read? Show your work.

Answer:

3+4+5+6+7+8+9 = 42 pages

Thus all students read 42 pages.

Question 8.

The table shows the heights of trees at a tree farm, to the nearest foot. Make a dot plot for the tree heights.

Answer:

Given data,

Fraser fir – 6, 7, 10, 11, 14, 8, 10, 13, 12, 7

Douglas fir – 15, 14, 12, 16, 13, 11, 12, 15, 16, 18

Blue Spruce – 10, 12, 14, 9, 10, 8, 11, 12, 8, 10

**Lesson 14.2 More Practice/Homework**

Question 1.

The ages of campers at a summer camp that have attended camp for at least five years are listed.

13, 12, 15, 14, 16, 13, 15, 14, 15, 16, 15, 14, 12, 14, 16, 13, 15, 12, 14,

A. Complete the dot plot for the campers’ ages.

Answer:

Given,

13, 12, 15, 14, 16, 13, 15, 14, 15, 16, 15, 14, 12, 14, 16, 13, 15, 12, 14,

B. What is the most common age of the campers?

Answer: 14 and 15 is the most common age of the campers.

C. How many observations are shown in the dot plot?

Answer: There are 19 observations shown in the dot plot.

D. Attend to Precision What percent of campers are over the age of 14?

Answer: 50 percent of campers are over the age of 14.

Question 2.

**STEM** A zoo has a population of endangered leaf-tailed geckos. Each year, the zoo records the number of eggs each female gecko lays and hatches. The data shown in the dot plot show the number of eggs hatched in a year.

A. What is the total number of eggs hatched in one year? Explain how you found your answer.

Answer:

As per the data shown in the dot plot we can say that there are 16 eggs hatched in one year.

B. What is the total number of geckos that laid eggs that hatched?

Answer: 16 is the total number of geckos that laid eggs that hatched.

C. What is the greatest number of eggs laid and hatched by one gecko?

Answer: 6 is the greatest number of eggs laid and hatched by one gecko.

D. What is the most common number of eggs hatched?

Answer: 6 is the most common number of eggs hatched.

E. **Reason** One of the zoologists splits the data and considers the top half of the data, or the 8 greatest observations. What percent of the total eggs is under consideration? Explain your reasoning.

Answer:

**Test Prep**

Question 3.

The chart shows the average daily temperatures for a week in a town. Which dot plot best represents the information in the table?

Answer:

As per the table, there are three 86, two 88, 84, 92.

Option B is the correct answer.

Question 4.

The dot plot shows the concentrations of salt in samples of seawater from around the world.

A. How many samples were taken?

Answer: According to the dot plot shown above there are 17 samples were taken.

B. What fraction of the samples have a salt content greater than 38 grams?

Answer: 6/17 of the samples have a salt content greater than 38 grams.

**Spiral Review**

Question 5.

A rectangular prism has a volume of 990 cubic inches. If it has a height of 11 inches and a width of 10 inches, what is its length?

Answer:

Given,

A rectangular prism has a volume of 990 cubic inches

Height = 11 in.

Width = 10 in.

Volume of the rectangular prism = lwh

990 = l × 11 × 10

l = 990/110 = 9 in

Thus the length of the rectangular prism is 9 inch.

Question 6.

Write an equation for the statement: A kilogram is equal to approximately 2.2 pounds. A cinder block weighs x pounds. A brick has a mass of 0.6 kilograms. What is the total mass in kilograms y of the cinder block and brick?

Answer:

A kilogram is equal to approximately 2.2 pounds.

A cinder block weighs x pounds.

Brick has a mass of 0.6 kilograms.

1 kg = 2.2 pounds

1 pound = 1/2.2

y = x (pounds) + 0.6 kg

y = x(1/2.2 kg) + 0.6 kg

y = 0.45x kg + 0.6 kg

Thus the total mass in kilograms y of the cinder block and brick is y = 0.45x + 0.6

Question 7.

Evaluate the expression 3x^{2} + 4x^{3} when x = 4.

Answer:

3x^{2} + 4x^{3} when x = 4

3(4)^{2} + 4(4)^{3} = 3 × 16 + 4 × 64

48 + 256 = 304