Start Your Day the Right Way - Folsom Cordova Unified School District

[Pages:34]Lesson 8.1 Skills Practice

8

Name

Start Your Day the Right Way

Graphically Representing Data

Vocabulary

Choose the term that best completes each statement.

dot plot symmetric histogram box-and-whisker plot

five number summary discrete data skewed right bin

Date

data distribution skewed left frequency continuous

1. A(n)

histogram

is a graphical way to display quantitative data using vertical bars.

2. A data distribution is

skewed right

if the peak of the data is to the left side of the graph

with only a few data points to the right side of the graph.

3.

Discrete data

"counted."

are data that have only a finite number of values or data that can be

4. A(n) box-and-whisker plot displays the data distribution based on a five number summary.

5. The overall shape of a graph which shows the way in which data are spread out or clustered together is called the data distribution .

6.

Continuous data are data which can take any numerical value within a range.

7. A data distribution is

skewed left

if the peak of the data is to the right side of the graph

with only a few data points to the left side of the graph.

8. A(n)

dot plot

number line.

is a graph that shows how discrete data are distributed using a

9. For a set of data, the five number summary consists of the minimum value, the first quartile, the median, the third quartile, and the maximum value.

10. A data distribution is

symmetric

if the peak of the data is in the middle of the graph.

The left and right sides of the graph are nearly mirror images of each other.

11. The number of data values included in a given bin of a data set is called

frequency

.

12. The bar width in a histogram that represents an interval of data is often referred to as

a

bin

.

Chapter 8 Skills Practice 453

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Problem Set

Construct the graphical display for each given data set. Describe the distribution of the data.

1. Construct a dot plot to display the scores on a recent math quiz. The data are 12, 14, 8, 13, 12, 14, 5, 13, 14, 3, 15, 15, 10, 13, 12, 0, 14, 11, 14, 13, and 10.

X

XX

XX X

X

XX X X

X

X

X

X

X X XX X X

01234

The data are skewed left.

5 6 7 8 9 10 11 12 13 14 15 Math Quiz Scores

2. Construct a dot plot to display the number of canned goods donated by each student during a charity event. The data are 15, 18, 18, 22, 13, 15, 19, 17, 18, 17, 16, 10, 17, 20, 19, 25, 17, 18, 19, and 16.

XX

XXX

XXXXX

X

X

XXXXXX

X

X

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Number of Canned Goods Donated per Student

The data are symmetric.

3. Construct a dot plot to display the number of items purchased by a number of randomly chosen customers at a toy store. The data are 2, 4, 3, 7, 12, 3, 1, 5, 6, 3, 4, 2, 4, 3, 7, 14, 10, 3, 5, and 9.

X

X

XX

XXXX

X

XXXXXXX

XX

X

X

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Number of Items Purchased per Customer

The data are skewed right.

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Name

Date

4. Construct a box-and-whisker plot to display the number of pets owned by a number of randomly chosen students. The data are 2, 0, 5, 1, 2, 1, 0, 8, 4, 3, 9, 1, 2, 3, and 1.

0

1

2

3

4

5

6

7

8

9

10

Number of Pets Owned

The data are skewed right.

5. Construct a box-and-whisker plot to display the scores on a recent science test. The data are 90, 95, 100, 70, 85, 65, 90, 80, 65, 70, 75, 80, 85, 80, 60, 80, 75, and 85.

60

65

70

75

80

85

90

95

100

Science Test Scores

The data are symmetric.

6. Construct a box-and-whisker plot to display the number of miles from school that a number of randomly chosen students live. The data are 5, 10, 15, 12, 1, 14, 9, 15, 3, 10, 12, 15, 8, 14, 13, and 2.

01234

The data are skewed left.

5 6 7 8 9 10 11 12 13 14 15 Miles from School

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7. Construct a histogram to display the circumferences of the pumpkins in the Jeffiers' family pumpkin crop. The data are 22.1, 35.6, 15.8, 36.9, 40.0, 28.5, 38.4, 20.4, 25.8, 34.1, 39.9, 42.2, 24.3, 22.7, 19.8, 27.9, 22.2, 34.3, 40.4, 20.6, 38.2, and 18.1. Use 10 # x , 20 as the first interval.

Jef ers' Family Pumpkin Crop 10

9

8

Number of Pumpkins

7

6

5

4

3

2

1

0

10

20

30

40

50

Circumference (inches)

The data are symmetric.

8. Construct a histogram to display the scores on a recent English quiz. The data are 18, 45, 20, 32, 9, 35, 49, 28, 25, 19, 5, 30, 22, 24, and 14. Use 0 # x , 10 as the first interval.

English Quiz Scores 5

4

Number of Students

3

2

1

0 0

10 20 30 40 50 Quiz Score

The data are symmetric.

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Name

Date

Analyze the given dot plot which displays the number of home runs by each of the girls on the softball team this season. Use the dot plot to answer each question.

Softball Team Home Runs

X

XX

XXX

X

XXX

X

XX

X

0 1 2 3 4 5 6 7 8 9 10 11 12

Number of Home Runs

9. Describe the distribution of the data in the dot plot and explain what it means in terms of the problem situation.

The data are skewed right, because a majority of the data values are on the left of the plot and only a few of the data values are on the right of the plot. This means that a majority of the players on the softball team hit a small number of home runs, while only a few players on the team hit a large number of home runs.

10. How many players are on the softball team? There are 14 players on the softball team.

11. How many players hit more than 2 home runs? Five players hit more than 2 home runs.

12. How many players hit at least 1 home run? Ten players hit at least 1 home run.

13. How many players hit more than 1 and fewer than 9 home runs? Six players hit more than 1 and fewer than 9 home runs.

14. How many players scored more than 12 home runs? No players scored more than 12 home runs.

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Analyze the given box-and-whisker plot which displays the heights of 40 randomly chosen adults. Use the box-and-whisker plot to answer each question.

Heights of 40 Randomly Chosen Adults

55

60

65

70

75

80

Height (inches)

15. What is the height range of the middle 50 percent of the surveyed adults? The middle 50 percent of the surveyed adults are at least 65 inches and at most 72 inches tall.

16. How many of the surveyed adults are exactly 68 inches tall? It is not possible to determine the number of surveyed adults who are exactly 68 inches tall.

17. What percent of the surveyed adults are 68 inches tall or shorter? Fifty percent of the surveyed adults are 68 inches tall or shorter.

18. What is the height of the tallest adult surveyed? The tallest adult surveyed is 79 inches tall.

19. How many of the surveyed adults are at least 58 inches tall? One hundred percent of the surveyed adults are at least 58 inches tall. Therefore, all 40 of the surveyed adults are at least 58 inches tall.

20. Describe the distribution of the data in the box-and-whisker plot and explain what it means in terms of the problem situation.

The data are symmetric, because the data are clustered around the center of the data values. Twenty-five percent of the data are in the lowest 7 inch range and twenty-five percent of the data are in the highest 7 inch range. Fifty percent of the data are in the middle 7 inch range.

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Name

Date

Analyze the given histogram which displays the ACT composite score of several randomly chosen students. Use the histogram to answer each question.

ACT Composite Scores 10

9

8

Number of Students

7

6

5

4

3

2

1

0 10 15 20 25 30 35

ACT Composite Score

21. How many students are represented by the histogram? There are a total of 31 students represented by the histogram.

22. Describe the distribution of the data in the histogram and explain what it means in terms of the problem situation.

The data are symmetric, because a majority of the values are in the middle while the remaining values are spread out approximately evenly on both sides of the middle. Most of the students scored in the middle range of values while a smaller number of students had a very low or very high score.

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23. How many of the students had an ACT composite score of exactly 25? It is not possible to determine the number of students who scored exactly 25.

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24. How many of the students had an ACT composite score of at least 20? Twenty students had an ACT composite score of at least 20.

25. How many of the students had an ACT composite score less than 30? Twenty-six students had an ACT composite score less than 30.

26. How many more students had an ACT composite score between 15 and 20 than had a composite score between 30 and 35?

Two more students had an ACT composite score between 15 and 20 than had a composite score between 30 and 35.

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