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L E S S O N 1.1 • Statistics: The Science and Art of Data 9

Lesson 1.1

W h A t D i D y O u L e A r n ?LEARNING TARGET ExAMPLES ExERCISES

Identify the individuals and variables in a data set, then classify the variables as categorical or quantitative.

p. 6 1–4

Summarize the distribution of a variable with a frequency table or a relative frequency table.

p. 7 5–8

The solutions to all exercises numbered in red are found in the Solutions Appendix, starting on page S-1.

Mastering Concepts and Skills

1. Box-office smash According to the Internet Movie Database, Avatar is tops based on box-office re-ceipts worldwide. The table displays data on sev-eral popular movies.5 Identify the individuals and variables in this data set. Classify each variable as categorical or quantitative.

Movie Year RatingTime (min) Genre Box office ($)

Avatar 2009 PG-13 162 Action 2,783,918,982

Titanic 1997 PG-13 194 Drama 2,207,615,668

Star Wars: The Force Awakens

2015 PG-13 136 Adventure 2,040,375,795

Jurassic World

2015 PG-13 124 Action 1,669,164,161

Marvel’s The Avengers

2012 PG-13 142 Action 1,519,479,547

Furious 7 2015 PG-13 137 Action 1,516,246,709

The Aveng-ers: Age of Ultron

2015 PG-13 141 Action 1,404,705,868

Harry Potter and the Deathly Hallows: Part 2

2011 PG-13 130 Fantasy 1,328,111,219

Frozen 2013 PG 108 Animation 1,254,512,386

Iron Man 3 2013 PG-13 129 Action 1,172,805,920

2. Tournament time A high school’s lacrosse team is planning to go to Buffalo for a three-day tour-nament. The tournament’s sponsor provides a list of available hotels, along with some information about each hotel. The following table displays data about hotel options. Identify the individuals and variables in this data set. Classify each variable as categorical or quantitative.

Hotel PoolExercise room?

Internet ($/day)

Restau- rants

Dis-tance

to site (mi)

Room service?

Room rate ($/

day)

Comfort Inn

Out Y 0 1 8.2 Y 149

Fairfield Inn & Suites

In Y 0 1 8.3 N 119

Baymont Inn & Suites

Out Y 0 1 3.7 Y 60

Chase Suite Hotel

Out N 15 0 1.5 N 139

Court-yard

In Y 0 1 0.2 Dinner 114

Hilton In Y 10 2 0.1 Y 156

Marriott In Y 9.95 2 0.0 Y 145

3. Portraits in data The table displays data on 10 ran-domly selected U.S. residents from a recent census. Identify the individuals and variables in this data set. Classify each variable as categorical or quantitative.

State

number of family members age Gender

Marital status

Yearly income

Travel time to

work (min)

Kentucky 2 61 Female Married $31,000 20

Florida 6 27 Female Married $31,300 20

Wisconsin 2 27 Male Married $40,000 5

California 4 33 Female Married $36,000 10

Michigan 3 49 Female Married $25,100 25

Virginia 3 26 Female Married $35,000 15

Pennsylvania 4 44 Male Married $73,000 10

Virginia 4 22 Male Never married/

single

$13,000 0

California 1 30 Male Never married/

single

$50,000 15

New York 4 34 Female Separated $40,000 40

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Exercises Lesson 1.1

Starnes_3e_CH01_002-093_v4.indd 9 27/06/16 1:50 PM

(C) 2017 BFW Publishers

C H A P T E R 1 • Analyzing One-Variable Data10

4. Who buys cars? A new-car dealer keeps records on car buyers for future marketing purposes. The table gives information on the last 4 buyers. Identify the individuals and variables in this data set. Classify each variable as categorical or quantitative.

Buyer’s name

Zip code Gender

Buyer’s distance

from dealer

(mi)Car

modelEngine type (cylinders) Price

P. Smith 27514 M 13 Fiesta 4 $26,375

K. Ewing 27510 M 10 Mustang 8 $39,500

L. Shipman 27516 F 2 Fusion 4 $38,400

S. Reice 27243 F 4 F-150 6 $56,000

5. Choose your power The online survey (page 6) also asked which superpower students would choose to have—fly, freeze time, invisibility, super strength, or telepathy (ability to read minds). Here are the re-sponses from the 40 students in the sample. Summa-rize the distribution of superpower preference with a frequency table and a relative frequency table.

Fly Freeze time Telepathy Fly Telepathy

Super strength

Telepathy Telepathy Fly Super strength

Invisibility Freeze time Fly Telepathy Freeze time

Telepathy Super strength

Fly Freeze time Telepathy

Freeze time

Freeze time Freeze time Fly Fly

Fly Freeze time Invisibility Fly Invisibility

Telepathy Telepathy Fly Telepathy Fly

Fly Telepathy Telepathy Fly Fly

6. Birth months Here are the reported birth months for the 40 students in the online sample. Summa-rize the distribution of birth month with a frequen-cy table and a relative frequency table.

January March August April June

March January June November January

July December April April January

December May December December December

June August March January July

April July April June May

January August April October January

December March February July June

7. Get some sleep The online survey also asked how much sleep students got on a typical school night. Here are the responses from the 40 students in the sample (in hours). Summarize the distribution of sleep amount with a frequency table and a relative frequency table.

9 8 6 7.5 7 8 4 7 7 8

8 8 6 7 8 8 7 7 6 8

9 7 6 5 7 8 8.5 7 9 6

6 6.5 8 9 5 8 7 7 7 7

8. Crowded house? The online survey also asked how many people lived in the student’s home. Here are the responses from the 40 students in the sample. Summarize the distribution of household size with a frequency table and a relative frequency table.

3 5 3 2 4 6 4 4 3 5

4 4 2 2 4 4 3 4 3 3

5 3 5 5 4 4 4 5 3 3

3 4 3 3 4 3 2 6 2 4

Applying the Concepts

9. Where did you go? June and Barry are interested in where students at their school travel for spring break. So they survey 100 classmates who took a trip dur-ing spring break this year. Then they make a spread-sheet that includes the state or country visited, how many nights they spent there, mode of transportation to get to the destination, distance from home, and average cost per night for each student’s trip. Identify the individuals in this data set. Classify each variable as categorical or quantitative.

10. Protecting history How can we help wood surfaces resist weathering, especially when restoring historic wooden buildings? Researchers prepared wooden panels and then exposed them to the weather. Here are some of the variables recorded: type of wood (yellow poplar, pine, cedar); type of water repellent (solvent-based, water-based); paint thickness (in millimeters); paint color (white, gray, light blue); weathering time (in months). Identify the individu-als in this data set. Classify each variable as cat-egorical or quantitative.

11. Numerical but not quantitative Give two examples of variables that take numerical values but are cat-egorical.

12. Quantigorical? In most data sets, age is classified as a quantitative variable. Explain how age could be classified as a categorical variable.

13. Car stats Popular magazines rank car models based on their overall quality. Describe two categorical variables and two quantitative variables that might be considered in determining the rankings.

14. Social media You are preparing to study the social media habits of high school students. Describe two categorical variables and two quantitative variables that you might record for each student.

pg 7



L E S S O N 1.2 • Displaying Categorical Data 17

Lesson 1.2


Make and interpret bar charts of categorical data. p. 12 1–4

Interpret pie charts. p. 13 5–8

Identify what makes some graphs of categorical data deceptive. p. 15 9–12

4. Click on Begin Analysis. A bar chart of the data should be displayed.

5. To get a pie chart, change the plot type.


1. Radio frequencies? Arbitron, the rating service for ra-dio audiences, places U.S. radio stations into catego-ries that describe the kinds of programs they broad-cast. The frequency table summarizes the distribution of station formats in a recent year.9 Make a bar chart to display the data. Describe what you see.

Format Count of stations

Adult contemporary 2,536All sports 1,274Contemporary hits 1,012Country 2,893News/talk/information 4,077Oldies 831Religious 3,884Rock 1,636Spanish language 878Variety 1,579Other formats 4,852

2. What day were you born? The frequency table summarizes the distribution of day of the week for all babies born in a single week in the United States. Make a bar chart to display the data. Describe what you see.

Day Births

Sunday 7,374

Monday 11,704

Tuesday 13,169

Wednesday 13,038

Thursday 13,013

Friday 12,664

Saturday 8,459

3. Cool colors Popularity of colors for cars and light trucks changes over time. Silver passed green in 2000 to become the most popular color worldwide,

pg 12





then gave way to shades of white in 2007. Here is a relative frequency table that summarizes data on the colors of vehicles sold worldwide in 2014.10

ColorPercent of

vehicles ColorPercent of

vehicles

Black 19 Red 9

Blue 6 Silver 14

Brown/beige 5 White 29

Gray 12 Yellow/gold 3

Green 1 Other ??

(a) What percent of vehicles would fall in the “Other” category?

(b) Make a bar chart to display the data. Describe what you see.

(c) Would it be appropriate to make a pie chart of these data? Explain.

4. Slicing up spam E-mail spam is the curse of the In-ternet. Here is a relative frequency table that sum-marizes data on the most common types of spam.11

Type of spam Percent

Type of spam Percent

Adult 19 Leisure 6

Financial 20 Products 25

Health 7 Scams 9

Internet 7 Other ??

(a) What percent of spam would fall in the “Other” category?

(b) Make a bar chart to display the data. Describe what you see.

(c) Would it be appropriate to make a pie chart of these data? Explain.

5. Radio country Here is a pie chart of the radio station format data from Exercise 1. What percent of the graph does the “Country” slice make up? Justify your answer.

Oldies

Otherformats

Contemporaryhit

Adultcontemporary

All sports

Country

News/Talk/InfoReligious

Rock

Spanishlanguage

Variety

6. Friday’s child Here is a pie chart of the birthday data from Exercise 2. What percent of the graph does the “Friday” slice make up? Justify your answer.

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

7. What is your major? About 3 million first-year stu-dents enroll in U.S. colleges and universities each year. The pie chart displays data on the percent of first-year students who plan to major in several dis-ciplines.12 About what percent of first-year students plan to major in business? In education?

Arts

/Hum

aniti

es

Biological

sciences

Business

Education

Eng

ineerin

g

Physical sciences

Social sciences

Professional

Tech

nical

Other

8. Family origins Here is a pie chart of Census Bureau data to show the countries from which the more than 14 million Asians in the United States in 2010 descend.13 About what percent of Asians were of Chinese origin? Korean?

Other Asian

Chinese

Indian

FilipinoVietnamese

Korean

Japanese

pg 13



19L E S S O N 1.2 • Displaying Categorical Data

9. Game on! Students in a high school statistics class were given data about the favorite sport to play for a group of 35 girls. They produced the following pictograph. Explain how this graph is misleading.

Tennis

Soccer

Softball

Basketball

Spor

ts

Key:= 4 Players= 5 Players

= 2 Players

= 2 Players

10. Social media The Pew Research Center surveyed a random sample of U.S. teens and adults about their use of social media in 2013. The following pictograph displays some results. Explain how this graph is misleading.

13 –18 19–29 30 – 49

AGE BREAKDOWN (OF SOCIAL MEDIA USERS)

50 – 64 65 +

81%89%

78%

60%43%

11. Support the court? A news network reported the results of a survey about a controversial court decision. The network initially posted on its website a bar chart of the data similar to the one that follows. Explain how this graph is misleading. (Note: When notified about the misleading nature of its graph, the network posted a corrected version.)

63

62

61

60

59

58

57

56

55

54

53Democrats

Perc

ent w

ho a

gree

Republicans Independents

12. Your favorite subject? The bar chart shows the dis-tribution of favorite subject for a sample of 1000 high school juniors. Explain how this graph is mis-leading.

280260240220200180160

Num

ber

of s

tud

ents

140120100

Math Science English Socialstudies

Foreignlanguage

Finearts

Favorite subject


13. Frequent superpower? The online survey from Lesson 1.1 (page 6) asked which superpower high school students would choose to have—fly, freeze time, invisibility, super strength, or telepathy. Here are the responses from the 40 students in the sample. Make a relative frequency bar chart for these data. Describe what you see.

Fly Freeze time Telepathy Fly Telepathy

Super strength

Telepathy Telepathy Fly Super strength

Invisibility Freeze time Fly Telepathy Freeze time

Telepathy Super strength

Fly Freeze time

Telepathy

Freeze time Freeze time Freeze time Fly Fly

Fly Freeze time Invisibility Fly Invisibility

Telepathy Telepathy Fly Telepathy Fly

Fly Telepathy Telepathy Fly Fly

14. Birth months Here are the reported birth months for the 40 students in the online sample from Lesson 1.1 (page 6). Make a relative frequency bar chart for these data. Describe what you see.

January March August April June

March January June November January

July December April April January

December May December December December

June August March January July

April July April June May

January August April October January

December March February July June

15. Far from home A survey asked first-year college students, “How many miles is this college from your permanent home?” Students had to choose from the following options: 5 or fewer, 6 to 10, 11 to 50, 51 to 100, 101 to 500, or more than 500. The bar chart on the following page shows the percentage

pg 15




of students at public and private 4-year colleges who chose each option.14 Write a few sentences comparing the distributions of distance from home for students from private and public 4-year colleges who completed the survey.

5 orfewer

6 to 10 11 to50

51 to100

Distance from home (mi)

PublicPrivate

101 to500

Morethan500

0

5

10

15

20

25

30

35

Perc

ent

16. Vehicle colors—U.S. versus Europe Favorite vehicle colors may differ among countries. The bar chart displays data on the most popular car colors in a recent year for the United States and Europe. Write a few sentences comparing the distributions.

30

25

20

15

10

5

0White/pearl

Black Silver Blue Gray Red Beige/brown

Green Yellow/gold

Perc

ent

Color

U.S.Europe

Extending the Concepts

17. Pareto charts It is often more revealing to arrange the bars in a bar chart from tallest to shortest, moving from left to right. Some people refer to this type of bar chart as a Pareto chart, named after Italian economist Vilfredo Pareto. Make a Pareto chart for the data in Exercise 3. How is this graph more revealing than one with the bars ordered alphabetically?

18. Who goes to movies? The bar chart displays data on the percent of people in several age groups who attended a movie in the past 12 months:15

18–24 25–34 35–44 45–54 55–64 65–74 75 and older

Age group (years)

0

10

20

30

40

50

60

70

80

Perc

ent w

ho

atte

nd

ed a

mov

ie

(a) Describe what the graph reveals about movie attendance in the different age groups.

(b) Would it be appropriate to make a pie chart in this setting? Explain.

Recycle and Review

19. Skyscrapers (1.1) Here is some information about the tallest buildings in the world (completed by 2014).16 Identify the individuals and variables in this data set. Classify each variable as categorical or quantitative.

Building CountryHeight

(m) Floors useYear

completed

Burj Khalifa United Arab

Emirates

828 163 Mixed 2010

Shanghai Tower China 632 121 Mixed 2014

Makkah Royal Clock Tower Hotel

Saudi Arabia

601 120 Hotel 2012

One World Trade Center

United States

541 104 Office 2013

Taipei 101 Taiwan 509 101 Office 2004

Shanghai World Financial Center

China 492 101 Mixed 2008

International Commerce Center

China 484 118 Mixed 2010

Petronas Tower 1 Malaysia 452 88 Office 1998

Zifeng Tower China 450 89 Mixed 2010

Willis (Sears) Tower

United States

442 108 Office 1974



21

L e A r n i n g t A r g e t S

d Make and interpret dotplots of quantitative data.

d Describe the shape of a distribution.

d Compare distributions of quantitative data with dotplots.

Lesson 1.3

Displaying Quantitative Data: Dotplots

You can use a bar chart or pie chart to display categorical data. A dotplot is the sim-plest graph for displaying quantitative data.

D E F I N I T I O N Dotplot

A dotplot shows each data value as a dot above its location on a number line.

Figure 1.2 shows a dotplot of the number of siblings reported by each student in a statistics class. You’ll learn how to make and interpret dotplots in this lesson.

dddd

dddd

dd

d dddddddddddddddd

ddddddddddddd

Number of siblings

0 1 2 3 4 5 6 7

Making and Interpreting DotplotsFor small sets of quantitative data, it is fairly easy to make a dotplot by hand.

How to Make a Dotplot1. Draw and label the axis. Draw a horizontal axis and put the name of the quantitative

variable underneath.

2. Scale the axis. Find the smallest and largest values in the data set. Start the horizontal axis at a number equal to or less than the smallest value and place tick marks at equal intervals until you equal or exceed the largest value.

3. Plot the values. Mark a dot above the location on the horizontal axis corresponding to each data value. Try to make all the dots the same size and space them out equally as you stack them.

Remember what we said in Lesson 1.2: Making a graph is not an end in itself. When you look at a graph, always ask, “What do I see?”

Figure 1.2 Dotplot of data on the number of siblings reported by stu-dents in a statistics class.



L E S S O N 1.3 • Displaying Quantitative Data: Dotplots 27

Lesson 1.3


Make and interpret dotplots of quantitative data. p. 22 1–6

Describe the shape of a distribution. p. 24 7–10

Compare distributions of quantitative data with dotplots. p. 25 11–14


1. Magic words Here are data on the lengths of the first 25 words on a randomly selected page from Harry Potter and the Prisoner of Azkaban.

2 3 4 10 2 11 2 8 4 3 7 2 7

5 3 6 4 4 2 5 8 2 3 4 4

(a) Make a dotplot of these data.

(b) Explain what the dot above 6 represents.

(c) What percent of the words have more than 4 letters?

2. Frozen pizza Here are the number of calories per serving for 16 brands of frozen cheese pizza.18

340 340 310 320 310 360 350 330

260 380 340 320 310 360 350 330

(a) Make a dotplot of these data.

(b) Explain what the dot above 260 represents.

(c) What percent of the frozen pizzas have fewer than 330 calories?

3. How fuel efficient? Here are the EPA estimates of city gas mileage in miles per gallon (mpg) for the sample of 21 model year 2014 midsize cars.19 Make a dotplot of these data.

Model mpg Model mpg

Acura RLx 20 Kia Optima 20

Audi A8 18 Lexus ES 350 21

BMW 550i 17 Lincoln MKZ 22

Buick Lacrosse 18 Mazda 6 28

Cadillac CTS 18 Mercedes-Benz E350 21

Chevrolet Malibu 21 Nissan Maxima 19

Chrysler 200 21 Subaru Legacy 24

Dodge Avenger 21 Toyota Prius 51

Ford Fusion 22 Volkswagen Passat 24

Hyundai Elantra 28 Volvo S80 18

Jaguar xF 19

4. Gooooaaal! How good was the 2012 U.S. wom-en’s soccer team? With players like Abby Wam-bach, Megan Rapinoe, and Carli Lloyd, the team put on an impressive showing en route to win-ning the gold medal at the 2012 Summer Olym-pics in London. Here are data on the number of goals scored by the team in games played in the 12 months prior to the 2012 Olympics.20 Make a dotplot of these data.

1 3 1 14 13 4 3 4 2 5 2 0 4

1 3 4 3 4 2 4 3 1 2 4 2

5. Visualizing fuel efficiency The dotplot shows the difference (Highway – City) in EPA mileage ratings for each of the 21 model year 2014 midsize cars from Exercise 3.

–4 –2 0 2 4 6 8 10 12 14

Difference (Highway – City)

d dddd

dddd

d ddd

ddd

dd

ddd

(a) The dot above –3 is for the Toyota Prius. Explain what this dot represents.

(b) What percent of these car models get fuel effi-ciency of at least 10 mpg more on the highway than in the city?

6. Look at that gooooaaal! The dotplot shows the difference in the number of goals scored in each game (U.S. women’s team – Opponent) in Exercise 4.

d

ddd

ddd

ddd

dd

d d

ddd

dddddd d d

14121086420–2

Difference in goals (U.S. team – Opponent)

pg 22





(a) Explain what the dot above –1 represents.

(b) What percent of its games did the 2012 U.S. women’s team win?

7. Looking at the old How old is the oldest person you know? Prudential Insurance Company asked 400 people to place a blue sticker on a huge wall next to the age of the oldest person they have ever known. An image of the graph is shown here. De-scribe the shape of the distribution.

8. Off to school The dotplot displays data on the travel time to school (in minutes) reported by 50 Canadian students. Describe the shape of the distribution.

d ddddddddd

dddddd

ddddddd

dddd

ddd

dd

d d d dd

d d dd

d

dddddddd

0 20 40

Travel time (min)60 80 100

9. Pair-a-dice The dotplot shows the results of roll-ing a pair of 6-sided dice and finding the sum of the up faces 100 times. Describe the shape of the distribution.

Dice rolls2 4 6 8 10 12

dd

dd

dd

ddddddd

dddddddd

ddddddddddddddddddd

ddddddd

ddddddd

dddd

dddddd

dddddd

dd

ddddd

ddddd

ddd

ddd

dddddddddddd

10. Phone numbers The dotplot displays the last digit of 100 phone numbers chosen at random from a phone book. Describe the shape of the distribution.

Last digit0 2 4 6 8

dddddddd

dddddddddd

ddddddd

ddddddd

ddddddddd

dddddd

dddddd

dddddddddd

dddddddd

dddddddd

dd

ddddd

ddd

ddddddd

ddd

d

11. Making money The following parallel dotplots show the total family income of randomly chosen individuals from Indiana (38 individuals) and New Jersey (44 individuals). Compare the distributions of total family incomes in these two samples.

ddd dddd

ddd

ddd

ddddd

dddddd

d d dd dd d dd

ddd

ddd

dd

dd

ddd

d

dddd

dddd

ddd

dddd

d dd d dddd

dd

dd

dd

dd

dd

dd

Indiana

New Jersey0 25 50 75

Total family income ($1000)100 125 150 175

12. Movie lengths The following parallel dotplots display the lengths of the best 15 movies in each of three decades according to the Internet Movie Database (www.imdb.com). Compare the distribu-tions of movie lengths for these three time periods.

Dec

ade

Movie length (min)

1960–1969

1980–1989

2000–2009100 120 140 160 180 200 220

dd

dd d d dddd

d ddd

dd d

d d ddddd dd d dd d dd

ddd

ddd

ddd d dd d

13. Sugar high(er)? Researchers collected data on 76 brands of cereal at a local supermarket.21 For each brand, the values of several variables were recorded, including sugar (grams per serving), calories per serv-ing, and the shelf in the store on which the cereal was located (1 = bottom, 2 = middle, 3 = top). Here are parallel dotplots of the data on sugar content by shelf.

1

0 2 4 6

Sugars8 10 12 14 16

2

3

Shel

f

ddd

d d dd

dd

dd

dd

dddd

ddddd

ddd

dddd

dddddd

d d ddd

dddd

dddd

d dddd

ddd

ddd

dd

dd

d d

d d ddd

ddd

ddd

pg 24

pg 25



L E S S O N 1.3 • Displaying Quantitative Data: Dotplots 29

(a) Critics claim that supermarkets tend to put sugary kids’ cereals on lower shelves, where the kids can see them. Do the data from this study support this claim? Justify your answer.

(b) Is the variability in sugar content of the cereals on the three shelves similar or different? Justify your answer.

14. Enhancing creativity Do external rewards—things like money, praise, fame, and grades—promote cre-ativity? Researcher Teresa Amabile recruited 47 ex-perienced creative writers who were college students and divided them at random into two groups. The students in one group were given a list of statements about external reasons (E) for writing, such as public recognition, making money, or pleasing their parents. Students in the other group were given a list of state-ments about internal reasons (I) for writing, such as expressing yourself and enjoying playing with words. Both groups were then instructed to write a poem about laughter. Each student’s poem was rated sepa-rately by 12 different poets using a creativity scale.22 These ratings were averaged to obtain an overall cre-ativity score for each poem. Parallel dotplots of the two groups’ creativity scores are shown here.

Inte

rnal

(I)

Average rating

Rew

ard

0 5 10 15 20 25 30

Exte

rnal

(E)

ddd

d

dddddd

d

ddd

d ddd dd

dddd

d dd

dd

dd

dd dd

dddd

dd

d d dddd

(a) What do you conclude about whether external re-wards promote creativity? Justify your answer.

(b) Is the variability in creativity scores similar or different for the two groups? Justify your answer.


15. Bad dotplot Janie asked 10 friends how many pho-tos they posted on Instagram yesterday. Then she made the following dotplot to display the data. What’s wrong with Janie’s dotplot?

0 1 2 3 5 6 9 12Number of photographs

16. Another bad dotplot Herschel asked the students in his English class how many siblings they have. Then he made the following dotplot to display the data. What’s wrong with Herschel’s dotplot?

0 1 2Number of siblings

3 4 5 6

Recycle and Review

17. Brands that sell (1.1) The brands of the last 45 digi-tal single-lens reflex (SLR) cameras sold on a popu-lar Internet auction site are listed here. Summarize the distribution of camera brands with a frequency table and a relative frequency table.

Canon Sony Canon Nikon Fujifilm

Nikon Canon Sony Canon Canon

Nikon Canon Nikon Canon Canon

Canon Nikon Fujifilm Canon Nikon

Nikon Canon Canon Canon Canon

Olympus Canon Canon Canon Nikon

Olympus Sony Canon Canon Sony

Canon Nikon Sony Canon Fujifilm

Nikon Canon Nikon Canon Sony

18. Divorce American Style (1.2) The bar chart com-pares the marital status of U.S. adult residents (18 years old or older) in 1980 and 2010.23 Write a few sentences comparing the distributions of mar-ital status for these two years.

Marital status

70

60

50

40

30

20

10

0

Perc

ent

1980Never married

2010 1980Married

2010 1980Widowed

2010 1980Divorced

2010



L E S S O N 1.4 • Displaying Quantitative Data: Stemplots 35

Lesson 1.4

W h A t D i D y O u L e A r n ?

LEARNING TARGET ExAMPLES ExERCISES

Make stemplots of quantitative data. p. 31 1–4

Interpret stemplots. p. 32 5–8

Compare distributions of quantitative data with stemplots. p. 33 9–12


1. Science gets your heart beating! Here are the resting heart rates of 26 ninth-grade biology students. Make a stemplot of these data. Do not split stems.

61 78 77 81 48 75 70 77 70 76 86 55 65

60 63 79 62 71 72 74 74 64 66 71 66 68

2. Hot enough for you? Here are the high tempera-ture readings in degrees Fahrenheit for Phoenix, Arizona, for each day in July 2013. Make a stem-plot of these data. Do not split stems.

111 107 115 108 106 109 111 113 104 103 97

99 104 110 109 100 105 107 102 101 84 93

101 105 99 102 104 108 106 106 109

3. Something fishy As part of a study on salmon health, researchers measured the pH of 25 salmon fillets. Here are the data. Make a stemplot of these data using split stems.

6.34 6.39 6.53 6.36 6.39 6.25 6.45 6.38 6.33 6.26 6.24 6.37 6.32

6.31 6.48 6.26 6.42 6.43 6.36 6.44 6.22 6.52 6.32 6.32 6.48

4. Eat your beans! Beans and other legumes are a great source of protein. The following data give the protein content of 31 different varieties of beans, in grams per 100 grams of cooked beans.25 Make a stemplot of these data using split stems.

7.5 8.2 8.9 9.3 7.1 8.3 8.7 9.5 8.2 9.1 9.0 9.0

9.7 9.2 8.9 8.1 9.0 7.8 8.0 7.8 7.0 7.5 13.5 8.3

6.8 16.6 10.6 8.3 7.6 7.7 8.1

5. Science gets your heart beating! Here is a stemplot using split stems for the heart-rate data from Exercise 1.

4 855 56 012346 56687 00112447 5677898 18 6

(a) What percent of these ninth-grade biology students have resting heart rates below 70 beats per minute?

(b) Describe the shape of the distribution.

(c) Which value appears to be an outlier? Give the stemplot a key using this value.

6. Hot enough for you? Here is a stemplot using split stems for the daily high temperature in Phoenix data from Exercise 2.

8 489 39 799

10 01122344410 55666778899911 011311 5

(a) What percent of days in this month were hotter than 100 degrees Fahrenheit (°F)?


(c) Which value appears to be an outlier? Give the stemplot a key using this value.

7. Where are the older folks? Following is a stemplot of the percents of residents aged 65 and older in the 50 states and the District of Columbia.26

pg 31

pg 32





7 789 0

10 37911 4412 0233344589913 0223455555778888914 01233444568915 4916 017 3

KEY: 12|2 representsa state in which12.2% of residentsare 65 and older.

(a) What percent of states have more than 15% of resi-dents aged 65 and older?


(c) Which value appears to be an outlier? Can you guess what state this is?

8. South Carolina counties Here is a stemplot of the areas of the 46 counties in South Carolina. Note that the data have been rounded to the nearest 10 square miles (mi2).

3 99994 01166895 011155667786 478997 012455798 00119 13

10 811 23312 2

KEY: 6 | 4 represents acounty with an areaof 640 square miles(rounded to thenearest 10 mi2)

(a) What percent of South Carolina counties have ar-eas of less than 500 mi2?


(c) What is the area of the largest South Carolina county?

9. Basketball scores Here are the numbers of points scored by teams in the California Division I high school basketball playoffs in a single day’s games.27

71 38 52 47 55 53 76 65 77 63 65 63 68

54 64 62 87 47 64 56 78 64 58 51 91 74

71 41 67 62 106 46

On the same day, the final scores of games in Division V were as follows:

98 45 67 44 74 60 96 54 92 72 93 46

98 67 62 37 37 36 69 44 86 66 66 58

(a) Make a back-to-back stemplot to compare the points scored by the 32 teams in the Division I playoffs and the 24 teams in the Division V playoffs.

(b) In which of the two divisions did teams score more points in their playoff games? Justify your answer.

(c) Are the shapes of the distributions of points scored similar or different in the two divisions? Justify your answer.

10. Who’s taller? Who is taller, males or females? A sample of 14-year-olds from the United Kingdom was randomly selected. Here are the heights of the students (in centimeters).

Female160 169 152 167 164 163 160 163 169 157 158

153 161 165 165 159 168 153 166 158 158 166

Male154 157 187 163 167 159 169 162 176 177 151

175 174 165 165 183 180

(a) Make a back-to-back stemplot for these data.

(b) Who tends to be taller in the United Kingdom: 14-year-old females or 14-year-old males? Justify your answer.

(c) Are the shapes of the male and female distributions of height similar or different? Justify your answer.

11. Who hits the books more? Researchers asked the students in a large first-year college class how many minutes they studied on a typical weeknight. The back-to-back stemplot displays the responses from random samples of 30 women and 30 men from the class, rounded to the nearest 10 minutes. Write a few sentences comparing the male and female dis-tributions.

03333566689990222222255800344

001122

MenWomen

9622222222

8888888888755554440

0336 KEY: 2 | 3 = 230 min

12. Fill ’er up The back-to-back stemplot displays the prices for regular gasoline at stations in Reading, Pennsylvania, and Yakima, Washington, in spring 2014. Write a few sentences comparing the two dis-tributions.

799933355899993355799

363637373838

YakimaReading

9964

422999999776655

1

53939 KEY: 36 | 7 = $3.67

pg 33



L E S S O N 1.4 • Displaying Quantitative Data: Stemplots 37


13. Chasing food dollars A marketing consultant ob-served 50 consecutive shoppers at a supermarket to find out how much each shopper spent in the store. Here are the data (in dollars), arranged in increas-ing order:

3.11 8.88 9.26 10.81 12.69 13.78 15.23 15.62 17.00 17.39

18.36 18.43 19.27 19.50 19.54 20.16 20.59 22.22 23.04 24.47

24.58 25.13 26.24 26.26 27.65 28.06 28.08 28.38 32.03 34.98

36.37 38.64 39.16 41.02 42.97 44.08 44.67 45.40 46.69 48.65

50.39 52.75 54.80 59.07 61.22 70.32 82.70 85.76 86.37 93.34

(a) Round each amount to the nearest dollar. Then make a stemplot using tens of dollars as the stems and dollars as the leaves.

(b) Make another stemplot of the data by splitting stems. Which graph shows the shape of the distri-bution better?

(c) Write a few sentences describing the amount of money spent by shoppers at this supermarket.

14. What does ERA mean? One way to measure the ef-fectiveness of baseball pitchers is to use their earned run average, which measures how many earned runs opposing teams score, on average, every nine innings pitched. The overall earned run average for all pitchers in the major leagues in 2013 was 3.86. Here are the earned run averages for all 25 players who pitched for the Boston Red Sox in 2013.

3.75 3.52 4.57 4.32 1.74 1.09 3.16 1.81 2.64 3.77 4.04 4.97 4.86

5.34 4.88 4.62 3.86 3.52 5.56 3.60 8.60 5.40 6.35 9.82 9.00

(a) Truncate the hundredths place of each data value and make a stemplot, using the ones digit as the stem and the tenths digit as the leaf.

(b) Make another stemplot of the data by splitting stems. Which graph shows the shape of the distri-bution better?

(c) Write a few sentences describing the distribution of earned run averages of Boston’s pitchers in 2013.


Sometimes, the variability in a data set is so small that splitting stems in two doesn’t produce a stemplot that shows the shape of the distribution well. We can often solve this problem by splitting the stem into five parts, each consisting of two leaf values: 0 and 1, 2 and 3, 4 and 5, and so on.

Exercises 15 and 16 refer to the following setting. Here are the weights, in ounces, of 36 navel oranges selected from a large shipment to a grocery store.

5.7 5.4 5.8 5.3 4.6 4.9 5.6 5.3 5.5 5.5 5.4 5.8

5.3 5.5 5.5 5.4 5.8 5.9 5.4 5.1 5.0 5.5 5.7 4.9

5.0 5.3 5.1 5.2 5.7 5.6 5.8 4.5 5.2 5.4 5.7 5.6

15. Weights of oranges Make a stemplot of the data by splitting stems into two parts. Explain why this graph does not display the distribution of orange weights effectively.

16. Splitting the oranges Make a stemplot of the data by splitting stems into five parts. Describe the shape of the distribution.

Recycle and Review

17. More gas guzzlers (1.2) The EPA-estimated high-way fuel efficiency for four different sedans is given in the bar chart.28 Explain how this graph is mis-leading.

32

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20ToyotaCamry

BuickLaCrosse

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Mile

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allo

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HyundaiGenesis

FordTaurus

18. Comparing tuition (1.3) The dotplot shows the 2014 out-of-state tuition for the 40 largest colleges and universities in North Carolina.29 Describe the overall pattern of the distribution and identify any clear departures from the pattern.

5 10 15 20 25 30 35

Annual tuition ($1000)40 45 50

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4. Adjust the intervals to match those from the example and then graph the histogram.

d Press WINDOW . Enter the values shown.

d Press GRAPH .

d Press TRACE and to examine the intervals.

Lesson 1.5


Make histograms of quantitative data. p. 39 1–4

Interpret histograms. p. 41 5–8

Compare distributions of quantitative data with histograms. p. 42 9–12


1. Measuring carbon dioxide Burning fuels in power plants and motor vehicles emits carbon dioxide (CO2), which may contribute to global warming. The table displays CO2 emissions in metric tons per person from 48 countries with populations of at least 20 million.31 Make a histogram of the data using intervals of width 2, starting at 0.

Country CO2 Country CO2 Country CO2

Algeria 3.3 Egypt 2.6 Italy 6.7

Argentina 4.5 Ethiopia 0.1 Japan 9.2

Australia 16.9 France 5.6 Kenya 0.3

Bangladesh 0.4 Germany 9.1 Korea, North 11.5

Brazil 2.2 Ghana 0.4 Korea, South 2.9

Canada 14.7 India 1.7 Malaysia 7.7

China 6.2 Indonesia 1.8 Mexico 3.8

Colombia 1.6 Iran 7.7 Morocco 1.6

Congo 0.5 Iraq 3.7 Myanmar 0.2

Country CO2 Country CO2 Country CO2

Nepal 0.1 Russia 12.2 Turkey 4.1

Nigeria 0.5 Saudi Arabia

17.0 Ukraine 6.6

Pakistan 0.9 South Africa

9.0 United Kingdom

7.9

Peru 2.0 Spain 5.8 United States

17.6

Philippines 0.9 Sudan 0.3 Uzbekistan 3.7

Poland 8.3 Tanzania 0.2 Venezuela 6.9

Romania 3.9 Thailand 4.4 Vietnam 1.7

2. Off to work I go How long do people travel each day to get to work? The following table gives the average travel times to work (in minutes) for workers in each state and the District of Colum-bia who are at least 16 years old and don’t work at home.32 Make a histogram of the travel times using intervals of width 2 minutes, starting at 14 minutes.

pg 39




L E S S O N 1.5 • Displaying Quantitative Data: Histograms 45

State

Travel time to

work (min) State

Travel time to

work (min) State

Travel time to

work (min)

AL 23.6 LA 25.1 OK 20.0

AK 17.7 ME 22.3 OR 21.8

AZ 25.0 MD 30.6 PA 25.0

AR 20.7 MA 26.6 RI 22.3

CA 26.8 MI 23.4 SC 22.9

CO 23.9 MN 22.0 SD 15.9

CT 24.1 MS 24.0 TN 23.5

DE 23.6 MO 22.9 Tx 24.6

DC 29.2 MT 17.6 UT 20.8

FL 25.9 NE 17.7 VT 21.2

GA 27.3 NV 24.2 VA 26.9

HI 25.5 NH 24.6 WA 25.2

ID 20.1 NJ 29.1 WV 25.6

IL 27.9 NM 20.9 WI 20.8

IN 22.3 NY 30.9 WY 17.9

IA 18.2 NC 23.4

KS 18.5 ND 15.5

KY 22.4 OH 22.1

3. A bell curve? The IQ scores of 60 randomly selected fifth-grade students from one school are shown here.33

145 139 126 122 125 130 96 110 118 118

101 142 134 124 112 109 134 113 81 113

123 94 100 136 109 131 117 110 127 124

106 124 115 133 116 102 127 117 109 137

117 90 103 114 139 101 122 105 97 89

102 108 110 128 114 112 114 102 82 101

(a) Make a histogram that displays the distribution of IQ scores effectively.

(b) Many people believe that the distribution of IQ scores follows a “bell curve,” like the one shown at top right. Does the graph you drew in part (a) sup-port this belief? Explain.

4. Slow country tunes Here are the lengths, in min-utes, of the 50 most popular mp3 downloads of songs by country artist Dierks Bentley.

4.2 4.0 3.9 3.8 3.7

4.7 3.4 4.0 4.4 5.0

4.6 3.7 4.6 4.4 4.1

3.0 3.2 4.7 3.5 3.7

4.3 3.7 4.8 4.4 4.2

4.7 6.2 4.0 7.0 3.9

3.4 3.4 2.9 3.3 4.0

4.2 3.2 3.4 3.7 3.5

3.4 3.7 3.9 3.7 3.8

3.1 3.7 3.6 4.5 3.7

(a) Make a histogram that displays the distribution of song lengths effectively.

(b) Describe what you see.

5. Carbon dioxide emissions Refer to Exercise 1. The histogram displays the data using intervals of width 1.

00

2

4

6

8

10

12

3 6 9

CO2 emissions (metric tons per person)

Num

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of c

oun

trie

s

12 15 18

(a) In what percent of countries did CO2 emissions ex-ceed 10 metric tons per person?


(c) Which countries are possible outliers?

pg 41




6. Traveling to work Refer to Exercise 2. The histogram displays the data using intervals of width 1.

9

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5

4

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2

1

015 18 21 24 27 30

Average travel time (min)

Num

ber

of s

tate

s

(a) In what percent of states is the average travel time at least 20 min?


(c) Which two states are possible outliers with average travel times of less than 16 min?

7. Looking at returns on stocks The return on a stock is the change in its market price plus any dividend payments made. Total return is usually expressed as a percent of the beginning price. The figure shows a histogram of the distribu-tion of the monthly returns for all common stocks listed on U.S. markets over a 273-month period.34

Monthly percent return on common stocks

0

80

20

40

60

−25 −15 15−20 0 10−5−10 5

Num

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of m

onth

s

(a) A return less than zero means that stocks lost value in that month. About what percent of all months had returns less than zero?


(c) Identify the interval(s) that include(s) any possible outliers.

8. Healthy cereal? Researchers collected data on calories per serving for 77 brands of breakfast cereal. The following histogram displays the data.35

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060 70 80 90 100

Calories

Freq

uen

cy

110 120 130 140 150 160

(a) About what percent of the cereal brands have 130 or more calories per serving?


(c) Identify the interval(s) that include(s) any possible outliers.

9. Households and income Rich and poor households differ in ways that go beyond income. Here are his-tograms that display the distributions of household size (number of people) for low-income and high-income households.36 Low-income households had annual incomes less than $15,000, and high-income households had annual incomes of at least $100,000. Compare the distributions.

Household size, low income

0

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75 63 41 2

Perc

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Household size, high income

0

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Perc

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pg 42



L E S S O N 1.5 • Displaying Quantitative Data: Histograms 47

10. The statistics of writing style Numerical data can distinguish different types of writing and, some-times, even individual authors. Here are histo-grams that display the distribution of word length in Shakespeare’s plays and in articles from Popular Science magazine. Compare the distributions.

Number of letters in word

Shakespeare

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25

5

Perc

ent o

f wo

rds

1 3 5 7 9 112 4 6 8 10 12

1 3 5 7 9 112 4 6 8 10 12 13 14


Popular Science

Perc

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10

15

20

11. The shape of populations The following histograms show the distribution of age for 2015 in Vietnam and Australia from the U.S. Census Bureau’s inter-national database.

76543210

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Australia

Perc

ent i

n a

ge

gro

up

Age

98

6789

543210

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Perc

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n a

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gro

up

Age

Vietnam

(a) The total population of Australia at this time was 22,751,014. Vietnam’s population was 94,348,835. Why did we use percents rather than counts on the vertical axis of these graphs?

(b) What important differences do you see between the age distributions?

12. Who makes more: men or women? A manufactur-ing company is reviewing the salaries of its full-time employees below the executive level at a large plant. The following histograms display the distri-bution of salary for male and female employees:

300

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40 50 60 70

Salary ($1000)

Perc

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Men

300

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40 50 60 70

Salary ($1000)

Perc

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f wom

enWomen

(a) There were 756 female employees and 2451 male employees at the plant. Why did we use percents rather than counts on the vertical axis of these graphs?

(b) Do men or women tend to earn higher salaries at this plant? Justify your answer.


13. Off to school A random sample of 50 Canadian students was selected to complete an online survey in a recent year. The dotplot displays data on the travel time to school (in minutes) reported by each student. Make a histogram of the data. Describe what you see.

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14. Unprovoked gator! The dotplot shows the total number of unprovoked attacks by wild alligators on people in Florida in each year from 1971 to 2013. Make a histogram of these data. Describe what you see.

2 4 6 8 10 12 14 16

Attacks

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15. Communicate, eh? We chose a random sample of 50 Canadian students who completed an online survey that included the question “Which of these methods do you most often use to communicate with your friends?” The graph displays data on students’ responses. Jerry says that he would de-scribe this graph as skewed to the right. Explain why Jerry is wrong.

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Internetchat

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Textmessage

Method of communication

16. The Brooklyn Half The histogram shows the dis-tribution of age for runners in the Brooklyn, New York, half-marathon in 2013.37 Explain what is wrong with this histogram.

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012 20 25 30 35 40 45 50 55 60 70 80

Age

Perc

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17. Do the math The table gives the distribution of grades earned by students taking the AP® Calculus AB and AP® Statistics exams in 2014.38

Grade

5 4 3 2 1Total no. of exams

Calculus aB

72,332 48,873 51,950 31,340 89,577 294,072

Statistics 26,265 38,512 45,052 32,748 41,596 184,173

(a) Make an appropriate graphical display to compare the grade distributions for AP® Calculus AB and AP® Statistics.

(b) Write a few sentences comparing the two distribu-tions of exam grades.

18. Rolling the die Imagine rolling a fair, six-sided die 60 times. Draw a plausible graph of the distribu-tion of die rolls. Should you use a bar chart or his-togram to display the data?

Recycle and Review

19. Runs Scored (1.4) Listed here are the number of runs scored by players on the Chicago White Sox who played regularly during the 2013 season.39

24 41 46 68 46 43 84 57 60 38 14 15 19 8 7 4 6 7 2

(a) Make a stemplot of these data.

(b) Describe the shape of the distribution of runs scored.

20. Hot enough for you? (1.3) St. Louis, Missouri, and Washington, D.C., are at the same latitude, but are their summer temperatures similar? Here are dot-plots for each city of the high temperature on July 4 for the years from 1980 through 2013.40 Write a few sentences comparing the distributions of July 4 high temperature in these two cities.

St. Louis

Washington, D.C.70 75 80 85

High temperature on July 4, 1980 to 2013

90 95 100 105

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L E S S O N 1.6 • Measuring Center 55

L e S S O n A P P 1. 6

Is the pace of life slower in smaller cities?

Does it take less time to get to work in smaller cities? Here are the travel times in minutes for 15 workers in North Carolina, chosen at random by the Census Bureau, along with a dotplot of the data.44

30 20 10 40 25 20 10 60 15 40 5 30 12 10 10

0 5 10 15 20 25 30 35 40 45 50 55 60

Travel time to work (min)

d d d ddd

dd

dd

d dd

dd

1. Find the median. Interpret this value in context.

2. Calculate the mean travel time. Show your work.

3. Which measure of center—the median or the mean— better describes a typical travel time to work for this sample of workers in North Carolina? Justify your answer. ©

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Lesson 1.6


Find and interpret the median of a distribution of quantitative data. pp. 50, 51 1–4

Calculate the mean of a distribution of quantitative data. p. 52 5–8

Compare the mean and median of a distribution, and choose the more appropriate measure of center in a given setting.

p. 54 9–12


1. Quiz grades Joey’s first 13 quiz grades in a marking period are listed here. Find and interpret the median.

82 93 77 79 90 82 85 85 95 73 79 83 89

2. Big boys The roster of the Dallas Cowboys profes-sional football team in a recent season included 7 defensive linemen. Their weights (in pounds) were 321, 285, 300, 285, 286, 293, and 298. Find and interpret the median.

3. Large fries Ryan and Brent were curious about the amount of french fries they would get in a large order from their favorite fast-food restau-rant, Burger King. They went to several different Burger King restaurants over a series of days and ordered a total of 14 large fries. The weight of each order (in grams) is shown here. Find and interpret the median.

165 163 160 159 166 152 166 168 173 171 168 167 170 170

pg 50

pg 51





4. Carrots The weights (in grams) of 12 carrots in a single bag from a local grocery store are listed here. Find and interpret the median.

44 56 48 41 66 55 42 33 51 44 61 65

5. Skipped quiz Refer to Exercise 1.

(a) Calculate Joey’s mean quiz grade. Show your work.

(b) Joey has an unexcused absence for the 14th quiz, and he receives a score of zero. Recalculate the mean and median. Explain why the mean and me-dian are so different now.

6. Big outlier Refer to Exercise 2.

(a) Calculate the mean weight of the 7 defensive line-men. Show your work.

(b) The defensive lineman that weighed 321 pounds may be an outlier. How did this player affect the mean? Justify your answer with an appropriate calculation.

7. Mean fries Refer to Exercise 3.

(a) Calculate the mean weight for the 14 orders of large fries. Show your work.

(b) Ryan and Brent noticed a shortage of fries in the order that weighed 152 grams. How did this order affect the mean? Justify your answer with an ap-propriate calculation.

8. One more carrot Refer to Exercise 4.

(a) Calculate the mean weight of the carrots. Show your work.

(b) The 13th carrot in the bag weighed 93 grams. Recalculate the mean and median. Explain why the mean and median are so different now.

9. Birthrates in Africa One of the important factors in determining population growth rates is the birth-rate per 1000 individuals in a population. The dot-plot shows the birthrates per 1000 individuals for 54 African nations:

18 24 30

Birthrate (per 1000 population)36 42 48 54

d dd d d d d d d d dddd

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(a) Explain how the mean and median would compare.

(b) Which measure of center better describes a typical birthrate? Explain.

10. Electing the president To become president of the United States, a candidate does not have to receive a majority of the popular vote. The candidate does have to win a majority of the 538 electoral votes that are cast in the Electoral College. Here is a stem-plot of the number of electoral votes in 2016 for each of the 50 states and the District of Columbia.

KEY: 1 | 5 is a statewith 15 electoralvotes.

0 33333333444440 555666666777889991 000011112341 56682 002 9933 84455 5

(a) Explain how the mean and median would compare.

(b) Which measure of center better describes a typical number of electoral votes? Explain.

11. Smart kids The histogram displays the IQ scores of 60 randomly selected fifth-grade students from one school. Which measure of center is the more appropriate choice in this setting? Explain.

80

18

Num

ber

of s

tud

ents

IQ

16

14

12

10

8

6

4

2

90 100 110 120 130 140 150 160

12. Lightning The histogram displays data from a study of lightning storms in Colorado.45 It shows the distribution of time after midnight (in hours) until the first lightning flash for that day occurred. Which measure of center is the more appropriate choice in this setting? Explain.

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Time after midnight until first lightning flash (h)9 10 11 13 14 15 16 1712

0

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L E S S O N 1.6 • Measuring Center 57


13. Do adolescent girls eat fruit? We all know that fruit is good for us. Following is a histogram of the number of servings of fruit per day claimed by 74 seventeen-year-old girls in a study in Pennsyl-vania.46 Find the mean and median. Show your method clearly.

Servings of fruit per day

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ubje

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0 2 4 6 81 3 5 7

14. Shakespeare The following histogram shows the dis-tribution of lengths of words used in Shakespeare’s plays.47 Find the mean and median. Show your method clearly.


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15. How much for that house? The mean and median selling prices of existing single-family homes sold in the United States in May 2014 were $260,700 and $213,600.48

(a) Which of these numbers is the mean and which is the median? Explain your reasoning.

(b) Write a sentence to describe how an unethical poli-tician could use these statistics to argue that May 2014 home prices were too high.

16. How mean is this salary? Last year a small accounting firm paid each of its five clerks $44,000, two junior accountants $100,000 each, and the firm’s owner $540,000. Write a sentence to describe how an unethical recruiter could use statistics to mislead prospective employees.

17. Baseball salaries, means and medians Suppose that a Major League Baseball team’s mean yearly salary for its players is $2.3 million and that the team has 25 players on its active roster.

(a) What is the team’s total annual payroll?

(b) If you knew only the median salary, would you be able to answer this question? Why or why not?

18. Mean or median? You are planning a party for 30 guests and want to know how many cans of soda to buy. Earl, the soda elf, offers to tell you either the mean number of cans guests will drink or the median number of cans. Which measure of center should you ask for? Why?


Another measure of center for a quantitative data set is the trimmed mean. To calculate the trimmed mean, order the data set from lowest to highest, remove the same number of data values from each end, and calculate the mean of the remaining values. For a data set with 10 values, for example, we can calculate the 10% trimmed mean by re-moving the maximum and minimum value. Why? Because that’s one value trimmed from each “end” of the data set out of 10 values, and 1/10 = 0.10 or 10%.

19. Shoes How many pairs of shoes does a typical teenage boy own? To find out, a group of statis-tics students surveyed a random sample of 20 male students from their large high school. Then they re-corded the number of pairs of shoes that each boy owned. Here are the data, along with a dotplot.

14 7 6 5 12 38 8 7 10 10 10 11 4 5 22 7 5 10 35 7

0 5 10 15 20Shoes

25 30 35 40

d d d d d d d ddd

dd ddd

d

dddd

(a) Calculate the mean of the distribution.

(b) Calculate the 10% trimmed mean.

(c) Why is the trimmed mean a better summary of the center of this distribution than the mean?

Recycle and Review

20. File sizes (1.3) How much disk space does your music use? Here are the file sizes (in megabytes) for 18 randomly selected files on Gabriel’s mp3 player.

2.4 2.7 1.6 1.3 6.2 1.3 5.6 1.1 2.2

1.9 2.1 4.4 4.7 3.0 1.9 2.5 7.5 5.0

(a) Make a dotplot to display the data.(b) Explain what the dot above the number 5 on your

dotplot represents.

(c) What percent of the files are larger than 2 megabytes?

(d) Use the dotplot to describe the shape of the distri-bution of file sizes.



L E S S O N 1.7 • Measuring Variability 65

Lesson 1.7


Find the range of a distribution of quantitative data. p. 59 1–4

Find and interpret the interquartile range. p. 61 5–8

Calculate and interpret the standard deviation. p. 62 9–12


1. Teens and shoes How many pairs of shoes does a typical teenage boy own? To find out, a group of statistics students surveyed a random sample of 20 male students from their large high school. Then they recorded the number of pairs of shoes that each boy owned. Here are the data, along with a dotplot. Find the range of the distribution.

14 7 6 5 12 38 8 7 10 10 10 11 4 5 22 7 5 10 35 7

0 5 10 15 20

Shoes25 30 35 40

d ddd

d dddd

d d d d d d dddd

d

2. Traveling Tarheels! Here are the travel times in minutes for 15 workers in North Carolina, chosen at random by the Census Bureau, along with a dot-plot of the data. Find the range of the distribution.

30 20 10 40 25 20 10 60 15 40 5 30 12 10 10

0 5 10 15 20 25 30 35 40 45 50 55 60

d d d dd

d dd

dd

d dd

dd


3. Heavy Cowboys The roster of the Dallas Cow-boys professional football team in a recent season included 7 defensive linemen. Their weights (in pounds) were 321, 285, 300, 285, 286, 293, and 298. Find the range of the distribution.

4. Pizza and calories Here are data on the number of calories per serving for 16 brands of frozen cheese pizza.52 Find the range of the distribution.

340 340 310 320 310 360 350 330

260 380 340 320 310 360 350 330

5. Shoes and teens Refer to Exercise 1. Find the inter-quartile range. Interpret this value in context.

6. Tarheels Refer to Exercise 2. Find the interquartile range. Interpret this value in context.

7. Cowboys Refer to Exercise 3. Find and interpret the interquartile range.

8. Frozen pizza Refer to Exercise 4. Find and interpret the interquartile range.

9. Well rested? The first four students to arrive for a first-period statistics class were asked how much sleep (to the nearest hour) they got last night. Their responses were 7, 7, 8, and 10. Calculate the stan-dard deviation. Interpret this value in context.

pg 59

pg 61

pg 62





10. The rate of metabolism A person’s metabolic rate is the rate at which the body consumes energy. Metabolic rate is important in studies of weight gain, dieting, and exercise. Here are the metabolic rates of 7 men who took part in a study of dieting. (The units are calories per 24 hours. These are the same calories used to describe the energy content of foods.) Calculate the standard deviation. Interpret this value in context.

1792 1666 1362 1614 1460 1867 1439

11. Phosphate in blood The level of various substances in the blood influences our health. Here are mea-surements of the level of phosphate in the blood of a patient, in milligrams of phosphate per deciliter of blood, made on 6 consecutive visits to a clinic. Calculate and interpret the standard deviation.

5.6 5.2 4.6 4.9 5.7 6.4

12. Foot lengths Here are the foot lengths (in centime-ters) for a random sample of seven 14-year-olds from the United Kingdom. Calculate and inter-pret the standard deviation.

25 22 20 25 24 24 28


13. Varying fuel efficiency The dotplot shows the dif-ference (Highway – City) in EPA mileage ratings for each of 21 model year 2014 midsize cars.

d ddd

dd

dd

ddddd

dddd

d ddd

–4 –2 2 4

Difference (Highway – City)6 8 10 12 140

(a) Find the interquartile range of the distribution. Interpret this value in context.

(b) Calculate and interpret the standard deviation.

(c) Which is the more appropriate measure of variabil-ity for this distribution: the interquartile range or the standard deviation? Justify your answer.

14. Another serving of carrots The dotplot shows the weights (to the nearest gram) of 12 carrots in a single bag from a local grocery store.

30 35 40 45

Weights (g)50 55 60 65 70

d d d dd

d d dd dd d

(a) Find the interquartile range of the distribution. Interpret this value in context.

(b) Calculate and interpret the standard deviation.

(c) Which is the more appropriate measure of variability for this distribution: the interquartile range or the standard deviation? Justify your answer.

15. Comparing SD Which of the following distribu-tions has a larger standard deviation? Justify your answer.

25

20

15

Freq

uen

cy

10

5

01 2 3 4 5 6 7 8

Variable A25

20

15

10

5

01 2 3 4 5 6 7 8

Variable B

16. Comparing SD The parallel dotplots show the lengths (in millimeters) of a sample of 11 nails pro-duced by each of two machines.53 As mentioned on page 60, both distributions have a range of 4 mm. Which distribution has the larger standard devia-tion? Justify your answer.

dd

d dd

dd

dd

d dd

ddd

dd

dddd

d

68 69 70 71 72

Length (mm)

Mac

hin

e

A

B

17. Properties of the standard deviation(a) Juan says that, if the standard deviation of a list is

zero, then all the numbers on the list are the same. Is Juan correct? Explain your answer.

(b) Letitia alleges that, if the means and standard de-viations of two different lists of numbers are the same, then all of the numbers in the two lists are the same. Is Letitia correct? Explain your answer.

18. SD contest This is a standard deviation contest. You must choose four numbers from the whole numbers 0 to 10, with repeats allowed.

(a) Choose four numbers that have the smallest pos-sible standard deviation.

(b) Choose four numbers that have the largest possible standard deviation.

(c) Is more than one choice possible in either part (a) or (b)? Explain.



L E S S O N 1.8 • Summarizing Quantitative Data: Boxplots and Outliers 67


19. Estimating SD The dotplot shows the number of shots per game taken by NHL player Sidney Crosby in his 81 regular season games in a recent season.54 Is the standard deviation of this distribution closest to 2, 5, or 10? Explain.

ddd

ddd

dddddd

dddddddddd

dddddddddddddddddd

d

ddddddddd

ddddddd

ddddd

dddd

dd

dd

dd

ddd

dd

dd

ddddddddddddd

Number of shots0 2 4 6 8 10

20. Will Joey pass? Joey’s first 14 quiz grades in a marking period had a mean of 85 and a standard deviation of 8.

(a) Suppose Joey makes an 85 on the next quiz. Would the standard deviation of his 15 quiz scores be greater than, equal to, or less than 8? Justify your answer.

(b) Suppose instead that Joey has an unexcused ab-sence and makes a 0 on the next quiz. Would the standard deviation of his 15 quiz scores be greater than, equal to, or less than 8? Justify your answer.

Recycle and Review

21. Hurricanes (1.5, 1.6) The histogram shows the dis-tribution of the number of Atlantic hurricanes in every year from 1851 through 2012.55

20

5

10

15

20

25

30

4 6 8 10 12 14 16

Number of hurricanes

Freq

uen

cy

(a) Describe the shape of the distribution.

(b) Which would be a better measure of the typical number of hurricanes per year: the mean or the median? Justify your answer.

22. Salty nuggets (1.3, 1.4) The sodium content, in mil-ligrams per 3-oz serving, for 22 brands of breaded chicken nuggets and tenders are given here.56

340 360 310 370 300 310 210 230 240 480 330

240 450 180 270 240 420 330 560 440 350 210

(a) Make a stemplot of these data using split stems.

(b) Make a dotplot of these data.

(c) Describe any features of the distribution that are better illustrated by one graph than by the other.

Lesson 1.8

Summarizing Quantitative Data: boxplots and Outliers

L e A r n i n g t A r g e t S

d Use the 1.5 × IQR rule to identify outliers.

d Make and interpret boxplots of quantitative data.

d Compare distributions of quantitative data with boxplots.




Lesson 1.8

W h A t D i D y O u L e A r n ?LEARNING TARGET ExAMPLES ExERCISESUse the 1.5 × IQR rule to identify outliers. p. 68 1–4

Make and interpret boxplots of quantitative data. p. 70 5–8

Compare distributions of quantitative data with boxplots. p. 72 9–12

3. Press ZOOM and select ZoomStat to display the parallel boxplots. Then press TRACE to view the five-number summary.


1. Outlier Cowboys The roster of the Dallas Cow-boys professional football team in a recent season included 7 defensive linemen. Their weights (in pounds) were 321, 285, 300, 285, 286, 293, and 298. Identify any outliers in the distribution. Show your work.

2. Musical megabytes How much disk space does your music use? Here are the file sizes (in megabytes) for 18 randomly selected files on Gabriel’s mp3 player. Identify any outliers in the distribution.

2.4 2.7 1.6 1.3 6.2 1.3 5.6 1.1 2.2

1.9 2.1 4.4 4.7 3.0 1.9 2.5 7.5 5.0

3. Pizza with outliers The dotplot shows the num-ber of calories per serving for 16 brands of frozen cheese pizza.58 Identify any outliers in the distribu-tion. Show your work.

260 280 300 320

Calories340 360 380 400

d d d d d d dd d d dd d

d dd

4. Electoral College outliers To become president of the United States, a candidate does not have to re-ceive a majority of the popular vote. The candidate does, however, have to win a majority of the 538 electoral votes that are cast in the Electoral College. Here is a stemplot of the number of electoral votes in 2016 for each of the 50 states and the District of Columbia. Identify any outliers in the distribution. Show your work.

KEY: 1 | 5 is a statewith 15 electoralvotes.

0 33333333444440 555666666777889991 000011112341 56682 002 9933 84455 5

5. No need to call According to a study by Nielsen Mobile, “Teenagers ages 13 to 17 are by far the most prolific texters, sending or receiving 1742 messages a month.” Mr. Williams, a high school

pg 68

pg 70




L E S S O N 1.8 • Summarizing Quantitative Data: Boxplots and Outliers 75

statistics teacher, was skeptical about this claim. So he collected data from his first-period statistics class on the number of text messages and calls they had sent or received in the past 24 hours. Here are the data:

0 7 1 29 25 8 5 1 25 98 9 0 26

8 118 72 0 92 52 14 3 3 44 5 42

(a) Make a boxplot to display the data.

(b) Explain how the graph in part (a) gives evidence to contradict the claim in the article.

6. Acing the first test Here are the scores of Mrs. Liao’s students on their first statistics test:

93 93 87.5 91 94.5 72 96 95 93.5 93.5 73 82 45 88 80 86

85.5 87.5 81 78 86 89 92 91 98 85 82.5 88 94.5 43


(b) How did the students do on Mrs. Liao’s first test? Use the graph from part (a) to help justify your answer.

7. Boxed Cowboys Refer to Exercise 1.


(b) Which measure of variability—the IQR or standard deviation—would you report for these data? Use the graph from part (a) to help justify your choice.

8. Variable memory Refer to Exercise 2.


(b) Which measure of variability—the IQR or stan-dard deviation—would you report for these data? Use the graph from part (a) to help justify your choice.

9. Fat sandwiches, skinny sandwiches The following boxplots summarize data on the amount of fat (in grams) in 12 McDonald’s beef sandwiches and 9 McDonald’s chicken or fish sandwiches. Compare the distributions of fat content for the two types of sandwiches.

Chi

cken

or fi

shBe

ef

0 10 20 30 40

Fat (g)

*

10. Get to work! The following boxplots summa-rize data on the travel times to work for 20 randomly chosen New Yorkers and 15 randomly chosen North Carolinians. Compare the distri-butions of travel time for the workers in these two states.

*

0 20 40 60 80


NC

NY

11. Energetic refrigerators In its May 2010 edition, Consumer Reports magazine rated different types of refrigerators, including those with bottom freez-ers, those with top freezers, and those with side freezers. One of the variables they measured was annual energy cost (in dollars). The following box-plots show the energy cost distributions for each of these types.

Top

Side

Bott

om

40 60 80 100

Energy cost120 140 160

* *

(a) What percentage of bottom freezers cost more than $60 per year to operate? What about side freezers and top freezers?

(b) Compare the energy cost distributions for the three types of refrigerators.

12. Income in New England The following boxplots show the total income of 40 randomly chosen households each from Connecticut, Maine, and Massachusetts, based on U.S. Census data from the American Community Survey for 2012.

0

Connecticut

Massachusetts

Maine

50 100 150 200

Annual household income ($1000)

250

*

*

300 350 400 450 500

(a) Approximately what percentage of households in the Maine sample had annual incomes below $50,000? What about households in Massachu-setts and Connecticut?

(b) Compare the distributions of annual incomes in the three states.

pg 72





13. Text or talk? In a September 28, 2008, article titled, “Letting Our Fingers Do the Talking,” the New York Times reported that Americans now send more text messages than they make phone calls. Mr. Williams was curious about whether this claim was valid for high school students. So he collect-ed data from his first-period statistics class on the number of text messages and calls they had sent or received in the past 24 hours. A boxplot of the dif-ference (Texts – Calls) in the number of texts and calls for each student is shown here. Do these data support the claim in the article about texting versus calling? Justify your answer.

Difference (Texts – Calls)

–20 120600 80 1004020

* * * *

14. Alligator bites The Florida Fish and Wildlife Con-servation Commission keeps track of unprovoked attacks on people by alligators, defining “major” attacks as those requiring hospital treatment or (rarely) resulting in death and “minor” attacks as those requiring, at most, first aid. A local tourist bureau claims that most attacks are minor. A box-plot of the difference (Major – Minor) in reported number of attacks for each year from 1971 through 2013 is given here.59 Do these data support the tourist bureau’s claim? Justify your answer.

−5 0

Major attacks – Minor attacks

** * *

5 10

15. SSHA scores Higher scores on the Survey of Study Habits and Attitudes (SSHA) indicate good study habits and attitudes toward learning. Here are scores for 18 first-year college women.

154 109 137 115 152 140 154 178 101

103 126 126 137 165 165 129 200 148

And the scores for 20 first-year college men:

108 140 114 91 180 115 126 92 169 146

109 132 75 88 113 151 70 115 187 104

(a) Make parallel boxplots to compare the distributions.

(b) Do these data support the belief that men and women differ in their study habits and attitudes toward learning? Give appropriate evidence to sup-port your answer.

16. Well connected Who has more contacts—males or females? The data show the number of contacts that a sample of high school students had in their cell phones.

Male124 41 29 27 44 87 85 260 290 31

168 169 167 214 135 114 105 103 96 144

Female 30 83 116 22 173 155 134 180 124 33

213 218 183 110

(a) Make parallel boxplots to compare the distribu-tions.

(b) Based on your graphs in part (a), which gender tends to have more contacts in their cell phones? Give appropriate evidence to support your answer.


17. Measuring skewness Here is a boxplot of the num-ber of electoral votes in 2016 for each of the 50 states and the District of Columbia, along with summary statistics. You can see that the distribu-tion is skewed to the right with 3 high outliers. How might we compute a numerical measure of skewness?

0 10 20 30

Electoral votes

40 50 60

* * *

Variable n Mean Minimum Q1 Median Q3 Maximum

Electoral votes

51 10.55 3.00 4.00 8.00 12.00 55.00

(a) One simple formula for calculating skewness

is maximum − medianmedian − minimum

. Compute this value for

the electoral vote data. Explain why this formula should yield a value greater than 1 for a right-skewed distribution.

(b) Choosing only from the summary statistics provid-ed below, define a formula for a different statistic that measures skewness. Compute the value of this statistic for the electoral vote data. What values of the statistic might indicate that a distribution is skewed to the right? Explain.



L E S S O N 1.9 • Describing Location in a Distribution 83

Lesson 1.9

W h A t D i D y O u L e A r n ?LEARNING TARGET ExAMPLES ExERCISESFind and interpret a percentile in a distribution of quantitative data. p. 78 1–4

Estimate percentiles and individual values using a cumulative relative frequency graph.

p. 80 5–8

Find and interpret a standardized score (z-score) in a distribution of quantitative data.

p. 82 9–12


1. Play ball! The dotplot shows the number of wins for each of the 30 Major League Baseball teams in the 2014 season:

60 65 70 75 80 85 90 95 100Wins

d dd dd

d ddd

d dd

d dddd dddd d dd

dd d d

dd

(a) Find the percentile for the Boston Red Sox, who won 71 games.

(b) The New York Yankees’ number of wins is at the 60th percentile of the distribution. Interpret this value in context. How many games did New York win?

2. Stand up tall The dotplot shows the heights of the 25 students in Mrs. Navard’s statistics class.

Height (in.)60 62 64 66 68 70 72 74

dd

ddd

d d d d dd

dd

dd

dd

d

ddd

ddd

d

(a) Find the percentile for Lynette, the student who is 65 in. tall.

(b) Asher’s height is at the 88th percentile of the distribu-tion. Interpret this value in context. How tall is Asher?

3. A boy and his shoes How many pairs of shoes does a typical teenage boy own? To find out, a group of statistics students surveyed a random sample of 20 male students from their large high school. Then they recorded the number of pairs of shoes that each boy owned. Here are the data.

14 7 6 5 12 38 8 7 10 10

10 11 4 5 22 7 5 10 35 7

(a) Martin is the student who reported owning 22 pairs of shoes. Find Martin’s percentile.

(b) Luis is at the first quartile Q1 of the distribution. How many pairs of shoes does Luis own?

4. Unlocked for sale The “sold” listings on a popu-lar auction website included 21 sales of used “unlocked” phones of one popular model. Here are the sales prices.

450 415 495 300 325 430 370

400 325 400 235 330 304 415

355 405 449 355 425 299 345

(a) Find the percentile of the phone that sold for $325.

(b) What was the sales price of the phone that was at the third quartile Q3?

5. Supermarket sweep The following figure is a cu-mulative relative frequency graph of the amount spent by a sample of 50 grocery shoppers at a store.

Cum

ulat

ive

rela

tive

freq

uen

cy (%

)

010203040

607080

50

90100

20 40 60 80 1000 30 50 70 9010

Amount spent ($)

d

d

d

d

d

dd

dd

d

(a) What is the percentile for the shopper who spent $19.50?

(b) Estimate and interpret the 80th percentile of the distribution.

6. Light life The following graph is a cumulative relative frequency graph showing the lifetimes (in hours) of 200 lamps.62

pg 78

pg 80





Cum

ulat

ive

rela

tive

freq

uen

cy (%

)

0

20

40

60

80

100

150013001100900700500Lifetimes (h)

(a) What is the percentile for a lamp that lasted 900 hours?

(b) Estimate and interpret the 60th percentile of this distribution.

7. Call me maybe? The graph displays the cumula-tive relative frequency of the lengths of phone calls made from the math department office at Gabalot High last month.

Cum

ulat

ive

rela

tive

fr

eque

ncy

(%)

0

20

40

60

80

100

0 45403530252015105Call length (min)

d d dd

d

d

d

d d dd

d

dd d

(a) About what percent of calls lasted 30 minutes or more?

(b) Estimate the interquartile range (IQR) of the distribution.

8. That tall? The graph displays the cumulative relative frequency of the heights (in inches) of college basket-ball players in a recent season.

60

100

75

50

25

065 70

Height (in.)Cum

ulat

ive

rela

tive

freq

uen

cy (%

)

75 80 85

(a) About what percent of players were at least 75 in. tall?

(b) Estimate the interquartile range (IQR) of the distribution.

9. The Nationals play During the 2014 season, the mean number of wins for Major League Baseball teams was 81 with a standard deviation of 9.6 wins. Find the standardized score (z-score) for the Washington Nationals, who won 96 games. Inter-pret this value in context.

10. Stand tall The heights of the 25 students in Mrs. Navard’s statistics class have a mean of 67 in. and a standard deviation of 4.29 in. Find the stan-dardized score (z-score) for Boris, a member of the class who is 76 in. tall. Interpret this value in context.

11. Where are the old folks? Based on data from the 2010 U.S. Census, the percent of residents aged 65 or older in the 50 states and the District of Columbia has mean 13.26% and standard deviation 1.67%.

(a) Find and interpret the standardized score (z-score) for the state of Colorado, which had 9.7% of its residents age 65 or older.

(b) The standardized score for Florida is z = 2.60. Find the percent of the state’s residents that were 65 or older.

12. Meaning of the Dow The Dow Jones Industrial Average (DJIA) is a commonly used index of the overall strength of the U.S. stock market. In 2013 the mean daily change in the DJIA for the 252 days that the stock markets were open was 13.59 points with a standard deviation of 94.05 points.

(a) Find and interpret the standardized score (z-score) for the change in the DJIA on May 7, 2013, which was 87.31 points.

(b) The standardized score for May 1, 2013, was z = –1.62. Find the change in the DJIA for that date.


13. Setting speed limits According to the Los Angeles Times, speed limits on California highways are set at the 85th percentile of vehicle speeds on those stretches of road. Explain to someone who knows little statistics what that means.

14. Percentile pressure Larry came home very excited after a visit to his doctor. He announced proudly to his wife, “My doctor says my blood pressure is at the 90th percentile among men like me. That means I’m better off than about 90% of similar men.” How should his wife, who is a statistician, respond to Larry’s statement?

15. Big or little? Mrs. Munson is interested to know how her son’s height and weight compare with those of other boys his age. She uses an online calculator to determine that her son is at the 48th percentile for weight and the 76th percentile for height. Explain to Mrs. Munson what these values mean.

16. Run faster Peter is a star runner on the track team. In the league championship meet, Peter records a time that would fall at the 80th percentile of all his race times that season. But his performance places him at the 50th percentile in the league champion-ship meet. Explain how this is possible. (Remember that lower times are better in this case!)

pg 82



85

17. SAT versus ACT During her senior year, Courtney took both the SAT and ACT. She scored 680 on the SAT math test and 27 on the ACT math test. Scores on the math section of the SAT vary from 200 to 800, with a mean of 514 and standard de-viation of 117. Scores on the math section of the ACT vary from 1 to 36, with a mean of 21.0 and a standard deviation of 5.3. Calculate Courtney’s standardized score on each test. Which of her two test scores was better? Explain.

18. Generational GPA Rebecca and her father both graduated from the same high school. When her fa-ther looked at Rebecca’s transcript, he noticed that her high school GPA (4.2) was higher than his high school GPA (3.9). After letting Rebecca gloat for a minute, he pointed out that there were no weight-ed grades when he went to school. To settle their argument, they called the registrar at the school and got information about the distribution of GPA in each of their graduation years. When the father graduated, the mean GPA was 2.8 with a standard deviation of 0.6. When Rebecca graduated, the mean GPA was 3.2 with a standard deviation of 0.7. Calculate Rebecca’s and her father’s standard-ized GPA. Who had the better GPA? Explain.

Extending the concepts

19. Medical exam results People with low bone den-sity have a high risk of broken bones. Currently, the most common method for testing bone density is dual-energy X-ray absorptiometry (DEXA). A patient who undergoes a DEXA test usually gets bone density results in grams per square centime-ter (g/cm2) and in standardized units.

Judy, who is 25 years old, has her bone density measured using DEXA. Her results indicate a bone density in the hip of 948 g/cm2 and a standardized

score of z = −1.45. In the population of 25-year-old women like Judy, the mean bone density in the hip is 956 g/cm2.63

(a) Judy has not taken a statistics class in a few years. Explain in simple language what the standardized score tells her about her bone density.

(b) Use the information provided to calculate the standard deviation of bone density in the popula-tion of 25-year-old women.

Recycle and Review

20. Birthrates in Africa (1.6, 1.7, 1.8) One of the impor-tant factors in determining population growth rates is the birthrate per 1000 individuals in a population. Here are a dotplot and five-number summary for the birthrates per 1000 individuals in 54 African nations.

18 24 30 36 42 48 54

Birthrate (per 1000 population)

d d d d d ddd

d d d d d d dd

d dd

dd

d d ddddd

dd

dd

d

ddd

dd

d d dd

d

d dddd

dd

dd

dd

Minimum Q1 Median Q3 Maximum

14 29 37.5 41 53

(a) Construct a boxplot for these data.

(b) Suppose the maximum value of 53 was in error and should have been 45. For each statistic, indicate whether this correction would result in an increase, a decrease, or no change. Justify your answer in each case.

• Mean

• Median

• Standard deviation

• Interquartile range

Chapter 1

StAtS applied!Does hand sanitizer work?

recALL: Using 30 identical petri dishes, Daniel and Kate ran-domly assigned 10 students to press one hand in a dish after wash-ing with soap, 10 students to press one hand in a dish after using

hand sanitizer, and 10 students to press one hand in a dish after using nothing. After three days of incubation, the number of bacteria colonies on each petri dish was counted. Here are the data from Daniel and Kate’s experiment.

© Im

ager

ymaj

estic

/Ala

my

Stoc

k Ph

oto

Chapter 1 STATS applied!



wh diat d you learn?msgilfordmath.weebly.com/uploads/2/7/7/5/27753231/unit_1... · 2018-09-06 ·...

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