designing statistical questions -...

Chapter 15 Skills Practice • 809

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Why Do We Use Statistics?Designing Statistical Questions

VocabularyMatch each definition to its corresponding term.

1. A method for collecting information by asking statistical questions. a. data

2. An entire set of items from which data can be selected. b. statistical question

3. A characteristic of a population. c. population

4. The facts or numbers that describe the results of an experiment d. sample

or survey.

5. A question about a population or a sample. e. data analysis

6. A test performed to answer a question. f. parameter

7. Collecting, organizing, and analyzing data to answer statistical g. statistic

questions.

8. The characteristic of a sample. h. survey

9. A selection from a population. i. experiment

Lesson 15.1 Skills Practice

Name ________________________________________________________ Date _________________________

810 • Chapter 15 Skills Practice

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Problem SetDetermine whether each given question is a statistical question. If not, rewrite it to make it a

statistical question.

1. How many people in your class like to play video games?

This is a statistical question.

2. Is pizza your favorite food?

3. Do you usually go to bed before 10:00 pm on school nights?

4. How many of the students in your school were born in their current state of residence?

5. How much did you weigh when you were born?

6. Who is the fastest runner in your class?

Write two statistical questions that could be answered about each given topic by conducting a

survey or experiment.

7. vacation destinations

Answers may vary. “How many students in your class went to the beach last year

as a vacation destination?” “How many students in your class have ever traveled to

another country on vacation?”

8. sports

Lesson 15.1 Skills Practice page 2


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Name ________________________________________________________ Date _________________________

9. music

10. books

11. U. S. Presidents

12. pets

Determine whether a survey or an experiment would be the best way to answer each given

statistical question.

13. “How many of the students in your class ate breakfast this morning?”

A survey would be the best way to answer the statistical question.

14. “Which student in your school can run a 40-meter sprint the fastest?”

15. “How many students in your class can type at least 30 words per minute?”

16. “How many students in your class ride the bus to school each day?”


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17. “How many students in your class can hop on one leg while patting the top of their head with one

hand and rubbing their belly with the other hand?”

18. “How many of the teachers in your school enjoy fishing as a hobby?”

Determine whether each set of survey results are a parameter or a statistic.

19. According to an online poll, 35% of all U.S. citizens live in an apartment.

The results represent a statistic.

20. According to Ms. Carey’s survey of the students in her class, 50% of her students have at least

one dog.

21. A local newspaper conducted a survey last week. Of the 2300 subscribers, 1276 responded.

Based on the survey, the editor concludes that 95% of the newspaper’s subscribers will renew

their subscription next year.

22. According to a random telephone survey of 1000 residents of Jackson County, 43% of the

residents of Jackson County eat out at a restaurant more than once per week.

23. Mr. Rembrandt gives a survey to each of the students in the Art Club. He concludes that 90% of

the Art Club members would like to visit the High Museum of Art in Atlanta.

24. Each senior at Jackson County High School completes a survey. The principal concludes that 68%

of the students in the senior class have an after-school job.


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Name ________________________________________________________ Date _________________________

Dealing with DataCollecting, Displaying, and Analyzing Data

VocabularyWrite the term that best completes each statement.

1. A(n) is a way of displaying categorical data by using either horizontal or

vertical bars so that the height or length of the bars indicates the value for that category.

2. can only have values that are counting numbers.

3. A(n) is the number of times an item or number occurs in a data set.

4. Data for which each piece of data fits into exactly one of several different groups or categories are

called .

5. A(n) is a graph that shows how parts of the whole relate to the whole,

and how parts relate to other parts.

6. In a graph, the explains how each data set is represented by a color or

a pattern.

7. A(n) is used to display categorical data when each category contains

two different data sets. The two bars which represent each category are side by side, and space is

used to separate the categories.

8. are data which can be placed on a numerical scale.

9. A(n) is a graph in which the frequencies of two different groups for a

given category are stacked on top of one another in order to compare the parts to the whole.

10. can have values that are between two counting numbers.


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Problem SetDetermine whether each set of given data are categorical or quantitative. If the data are quantitative,

determine whether they are discrete or continuous.

1. Each student in your math class lists their favorite color.

The data are categorical.

2. Each student in your math class records their height to nearest quarter inch.

3. The points scored by Yuri during each academic team match of the season.

4. The members of the Horse Club list the types of horses they have.

5. The members of the Horse Club list the number of horses they have.

6. Each student in your class lists their favorite sport.

7. Each student in your class lists their favorite type of music.

8. Each student in your class lists the number of CDs they own.

9. Wallace lists the different types of animals that he observes on his nature walk.


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Name ________________________________________________________ Date _________________________

10. Each student in your class lists the distance they travel to school each day to the nearest

tenth of a mile.

Analyze the given graph to solve each problem.

11. On a recent trip to a beach in southern Florida, five friends competed to see who could find the

most sharks’ teeth. Their results are displayed in the bar graph.

Keith

Sarah

Caleb

Sam

Geraldine

Nam

e

12 14 16 18Number of Sharks’ Teeth Found

x

y

20 4 6 8 10

a. Who found the most sharks’ teeth? How many teeth did that person find?

Sam found the most teeth. He found 15 teeth.

b. How many total sharks’ teeth did the five friends find?

They found a total of 53 teeth.


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12. The double bar graph shows the scores of the five starters on the girls’ basketball team for

their Tuesday and Friday games.

Katelyn Jin Nora Brooke KianaPlayer Name

x

y Points Scored Tuesday and Friday

0

2

4

6

8

10

12

14

16

18

Po

ints

Sco

red

TuesdayFriday

a. Which player scored fewer points during Friday’s game than they did during Tuesday’s game?

b. Which player scored the most total points during the two games? How many points did that

player score?

c. Determine the average number of points scored by the five starters during Friday’s game.


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Name ________________________________________________________ Date _________________________

13. Four students participated in a Walk-a-Thon to raise money for a charity. The distances they each

walked on Saturday and Sunday are displayed in the stacked bar graph.

Miles Walked at the Walk-a-Thon

4

0

8

12

16

20

24

28

32

36M

iles

Wal

ked

Charlie Lisa Isaiah TabithaName

x

y

SundaySaturday

a. Who walked the most miles on Saturday? How many miles did that person walk on Saturday?

b. Who walked the most total miles during the Walk-a-Thon? How many total miles did that

person walk?


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14. The circle graph shows the results of the vote for the new school mascot.

Mascot Vote

Bears30%

Cheetahs20%Mustangs

15%

Tigers35%

a. If 400 students voted, how many students voted for the Cheetahs?

b. If the students who voted for the Mustangs would have voted for the Bears, would the outcome

of the election have been any different?

Create the specified graph for each given data set.

15. Create a single bar graph to display the scores of five students on a recent math quiz. Clayton

scored 18, Reginald scored 14, Ernestine scored 16, Maria scored 20, and Shawna scored 15.

2020 4 6 8 10 12 14 16 18Math Quiz Scores

Clayton

Reginald

Ernestine

Maria

Shawna

Nam

e


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Name ________________________________________________________ Date _________________________

16. Create a single bar graph to display the number of pets owned by each of the following students.

Aretha has 4 pets, Edward has 7 pets, Franco has 3 pets, and Patty has 5 pets.


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17. Create a double bar graph that displays the number of hours spent watching television

during the weekdays and during the weekend for five students last week.

Name

NumberofHoursWatchingTVDuringthe

Weekdays


Weekend

Sonya 12 6

Terrence 14 4

Will 6 0

Christine 8 3

Larry 10 5


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Name ________________________________________________________ Date _________________________

18. Create a stacked bar graph that displays the number of hours spent watching television during

the weekdays and during the weekend for five students last week.

Name


Weekdays


Weekend

Sonya 12 6

Terrence 14 4

Will 6 0

Christine 8 3

Larry 10 5


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19. Create a double bar graph to display the results of the prom theme vote.

PromTheme

NumberofJuniorVotes

NumberofSeniorVotes

Outer Space Romance 20 25

Texas Rodeo 30 35

Enchanted Ball 10 20

A Night in the 60s 15 25


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Name ________________________________________________________ Date _________________________

20. Create a stacked bar graph to display the results of the prom theme vote.

PromTheme

NumberofJuniorVotes

NumberofSeniorVotes

Outer Space Romance 20 25

Texas Rodeo 30 35

Enchanted Ball 10 20

A Night in the 60s 15 25


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Name ________________________________________________________ Date _________________________

At The OlympicsLine Plots and Stem-and-Leaf Plots

VocabularyWrite a definition for each of the following terms in your own words.

1. dot plot

2. distribution

3. symmetric

4. skewed right

5. skewed left

6. clusters


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7. gaps

8. stem-and-leaf plot

9. side-by-side stem-and-leaf plot

Problem SetIdentify the data distribution in the given plot as symmetric, skewed right, or skewed left. Identify any

clusters or gaps.

1.

0 1 2 3 4 5 6 7 8 9 10

The distribution is skewed right. There are clusters from 0 to 3

and from 5 to 6. There is a gap between 3 and 5.

2.

0 1 2 3 4 5 6 7 8 9 10


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Name ________________________________________________________ Date _________________________

3.

0 1 2 3 4 5 6 7 8 9 10

4.

0 1 2 3 4 5 6 7 8 9 10

5. Stem Leaves

0 7 8

1 2 4 8

2 1 1 6 8

3 0 2 3

4 2 3

Key: 1|2 5 12


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6. Stem Leaves

0 5 6 7 7 8 9

1 0 3 6 8 8

2 1 1 4 7

3 2 5

4 4

5

6 2

Key: 1|0 5 10

7. Data Set One Stem Data Set Two

9 8 5 3 3 2 3 2

8 6 4 3 4

7 6 2 5

6 1 4 4

9 8 7 2 5 7 9

0 8 0 2 2 5 6 8

9 0 0 1 2 3 3 5

Key: 9|3|2 5 39 and 32


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Name ________________________________________________________ Date _________________________

8. Data Set One Stem Data Set Two

8 1

5 2 2

9 7 5 3

8 4 3 3 2 4

6 5 5 5 2 4 5 6

1 6 1 3 7 8 8 9

7 0 2 3 3 5

Key: 1|0 5 10

Create a line plot, stem-and-leaf plot, or side-by-side stem-and-leaf plot displaying each given data set.

9. 1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 8, and 10

0 1 2 3 4 5 6 7 8 9 10

10. 0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 4, and 7

0 1 2 3 4 5 6 7 8 9 10


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11. 5, 7, 8, 9, 9, 10, 11, 13, 14, 18, 21, 26, 32, 39, and 42

12. 23, 41, 65, 57, 54, 28, 33, 40, 51, 41, 62, 42, and 49

13. 1.2, 1.3, 1.6, 1.9, 1.9, 2.0, 2.2, 2.3, 2.6, 2.7, 3.1, 3.2, 3.6, 3.6, 4.1, 4.2, 4.6, 5.0, 5.2, 5.3, 5.8,

and 6.2


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Name ________________________________________________________ Date _________________________

14. Data Set One: 2, 4, 4, 5, 5, 6, 8, 10, 11, 12, 14, 18, and 21

Data Set Two: 25, 29, 30, 33, 37, 41, 43, 43, 47, and 48

15. Data Set One: 35, 35, 40, 45, 50, 55, 60, 60, 65, 65, 65, 70, and 75

Data Set Two: 30, 35, 40, 45, 45, 45, 50, 50, 55, 55, 60, 65, and 70


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16. Data Set One: 4.6, 4.8, 5.1, 5.3, 5.9, 6.0, 6.1, 6.1, 6.5, 6.6, 6.8, 6.9, 7.2, 7.3, 7.7,

8.3, 8.5, 9.1, and 9.2

Data Set Two: 5.9, 6.2, 6.7, 7.0, 7.0, 7.3, 7.6, 7.6, 7.8, 7.9, 8.0, 8.1, 8.1, and 8.2


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Name ________________________________________________________ Date _________________________

Building UpUsing Histograms

VocabularyWrite a definition for each of the following terms in your own words.

1. histogram

2. frequency table


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Problem SetAnalyze the given histogram to solve each problem.

1. The histogram displays the number of homes sold by Really Real Realty

in 2009.

2

0

4

6

8

10

12

14

16

18

Jan–Mar Apr–Jun Jul–SepMonth

Oct–Dec

Num

ber

of

Ho

mes

So

ldHomes Sold by Really Real

Realty in 2009

a. During which 3-month interval did Really Real Realty sell the most

homes, and how many homes did they sell during that interval?

They sold the most homes during the April–June interval. They sold 15 homes

during that interval.

b. How many homes did Really Real Realty sell in 2009?

They sold 10 1 15 1 13 1 11, or 49, homes in 2009.



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2. The histogram displays the number of years of service for a sample of

U.S. Navy veterans.

5

0

10

15

20

25

30

35

Num

ber

of

Vet

eran

s

1–5 6–10 11–15 16–20 21–25

U.S. Navy Veterans Years of Service

Years of Service

a. How many veterans in the sample had more than 15 years of service?

b. How many veterans are represented by the histogram?


Name ________________________________________________________ Date _________________________


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3. The histogram displays the ages of U.S. Senators.

5

0

10

15

20

25

30

35

40–49 50–59 60–69

Num

ber

of

Sen

ato

rs

Age

Ages of U.S. Senators

70–79 80–89

a. How many U.S. Senators are in their sixties?

b. How many U.S. Senators are younger than 60?


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Name ________________________________________________________ Date _________________________

4. The histogram displays the number of graduates from various high

schools in Georgia for the year 2008.

5

0

10

15

20

25

30

35

0–99 100–199 200–299

Num

ber

of

Hig

h S

cho

ols

Number of Graduates

Number of GA Graduates per High School in 2008

300–399 400–499

a. How many high schools represented in the histogram had 300 or

more graduates in 2008?

b. How many high schools are represented in the histogram?


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Create a frequency table or a histogram for each given data set.

5. These data represent the number of employees at various restaurants in

New York City: 22, 35, 15, 26, 40, 28, 18, 20, 25, 34, 39, 42, 24, 22, 19, 27,

22, 34, 40, 20, 38, and 28. Use 10–19 as the first interval.

NumberofEmployeesatNewYorkCityRestaurants

NumberofEmployees Frequency(f)

10–19 3

20–29 11

30–39 5

40–49 3

6. These data represent the number of roller coasters at several major theme parks:

12, 15, 10, 13, 9, 17, 15, 7, 9, 10, 16, 12, 13, 8, 14, 9, 7, 13, and 15. Use 7–9 as

the first interval.


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Name ________________________________________________________ Date _________________________

7. Create a histogram based on the data in the frequency table.

NumberofBooksReadbyMembersoftheNovelIdeaBookClub

NumberofBooksRead Frequency(f )

0–9 7

10–19 13

20–29 9

30–39 2


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8. Create a histogram based on the data in the frequency table.

Test Scores for Mr. Watson’s Math Test

Test Score Frequency (f )

61–70 4

71–80 7

81–90 9

91–100 8



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9. Create a histogram for these data which represent the number of strep throat

cases reported by each doctor’s office in Jackson County last November: 3, 32,

27, 32, 32, 35, 46, 47, 15, 26, 22, 33, 19, 32, 7, 38, 40, 35, 35, 7, 47, 2, 6, 16,

19, 5, 28, 35, 20, 39, 3, 24, 14, 37, and 31. Use 0–9 as the first interval.

10. Create a histogram for these data which represent the greatest number of points

scored in a single game last season by the top 25 mens’ college basketball teams:

85, 101, 74, 99, 85, 99, 82, 75, 77, 89, 84, 86, 105, 82, 76, 75, 99, 101, 95, 93, 82,

102, 86, 74, and 88. Use 70–79 as the first interval.


Name ________________________________________________________ Date _________________________


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Analyze This!Designing and Implementing an Experiment

Problem Set 1. Mr. Bowman conducts an experiment with the students in his 6th grade physical education

class to test his hypothesis that practice can improve a person’s ability to make basketball

free throws. Each student attempts 10 free throws and Mr. Bowman records the number

of baskets each student makes. After one week of practice, each student attempts 10 free

throws and Mr. Bowman records the results again. The results of the experiment are displayed

in the table.

ResultsofMr.Bowman’sFreeThrowExperiment

Number of Free Throws Made Out of 10 Attempts Before the Week of Practice

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

Number of Free Throws Made Out of 10 Attempts After the Week of Practice

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


Name ________________________________________________________ Date _________________________


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a. Create a line plot for the results before the week of practice and a line plot for the

results after the week of practice.

0 1 2 3 4 5 6

Number of Free Throws Made Before One Week of Practice7 8 9

0 1 2 3 4 5 6

Number of Free Throws Made After One Week of Practice7 8 9

b. Describe the distribution of the data in each line plot and describe any clusters or gaps

that exist.

The distribution of the data in the first line plot is skewed right. There is a cluster of data

from 0 to 5 and a gap between 5 and 7. The distribution of the data in the second line plot

is symmetric. There is a cluster of data from 0 to 6 and a gap between 6 and 8.

c. What conclusions can you make about the experiment based on the data in your line plots?

Mr. Bowman’s hypothesis is correct. The data before the week of practice is skewed right

with most of the scores on the lower end of the plot. The data after the week of practice

is symmetric and centered around 4 free throws made.


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2. Ms. Yoon performs an experiment to determine whether her math students perform better on

tests when they are allowed to use a calculator. She gives 5 students a 20-point quiz and

doesn’t allow them to use a calculator. After they finish, she gives the same quiz to the

5 students and allows them to use a calculator. The results are displayed in the table.

Ms.Yoon’sMathQuizScores

StudentName QuizScorewithoutCalculator QuizScorewithCalculator

Rashad 12 15

Ben 15 16

Jenna 16 18

Omar 14 17

Kay 15 17

a. Create a double bar graph to display each student’s quiz scores.

b. What conclusions can you make about whether the use of a calculator helped the students

on their math quizzes?


Name ________________________________________________________ Date _________________________


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3. Shady Farms Tree Nursery conducts an experiment to determine which brand of fertilizer is

the best for their maple trees. They use a different brand of fertilizer on each of 5 different

maple tree saplings for a 2-year period. The amount of yearly growth is recorded in

the table.

ShadyFarmsMapleTreeGrowth

FertilizerUsed HeightGrowthinYear1(inches) HeightGrowthinYear2(inches)

Tree Top 15 15

Johnson’s 12 16

Big Tree 10 14

Sky High 15 17

Quick Grow 18 12

a. Create a stacked bar graph to display the results of the fertilizer experiment.

b. What conclusions can you make about which fertilizer is the best based on the

stacked bar graph?



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4. Ms. Smothers, the typing teacher, conducts an experiment to determine which computer-

based typing program produces the best results for her students. For one month, one of her

classes uses the Speedy Type program and a different class uses the Super Typer program.

Then, Ms. Smothers records the number of words per minute typed by each student in her classes.

The data are displayed in the table.

TypingResultsforMs.Smother’sStudents

Speedy Type (words per minute) 34, 38, 42, 29, 51, 43, 60, 42, 35, 48, 45, 54, 46, 26, 35, 44, 50, 40, 62, 55

Super Typer (words per minute) 32, 39, 41, 50, 25, 44, 38, 29, 40, 52, 34, 37, 37, 42, 27, 45, 46, 59, 35, 26

a. Create a side-by-side stem-and-leaf plot for the data.

b. Describe the distribution of the data in each data set.

c. Which typing program produced the best results according to the experimental data?


Name ________________________________________________________ Date _________________________

designing statistical questions -...

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