Starnes_3e_CH01_002-093_v2_LR_clean watermark

1

Analyzing
One-Varia

Lesson 1.1 Statistics: The Scie
Lesson 1.2 Displaying Catego
Lesson 1.3 Displaying Quanti
Lesson 1.4 Displaying Quanti
Lesson 1.5 Displaying Quanti
Lesson 1.6 Measuring Center
Lesson 1.7 Measuring Variabi
Lesson 1.8 Summarizing Qua
and Outliers
Lesson 1.9 Describing Locatio

Chapter 1 Main P
Chapter 1 Review
Chapter 1 Practic

2

Starnes_3e_CH01_002-093_v2.indd 2

g
able Data

ence and Art of Data 4
orical Data 11
itative Data: Dotplots 21
itative Data: Stemplots 30
itative Data: Histograms 38
r 49
ility 58
antitative Data: Boxplots
67
on in a Distribution 77

Points 86
w Exercises 88
ce Test 90

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Stats applied!

Does hand sanitizer work?

Is soap better than hand sanitizer for getting rid of u
signed an experiment to find out. Using 30 identica
10 students to press one hand in a dish after washin
hand in a dish after using hand sanitizer, and 10 stu
using nothing. After three days of incubation, they
nies on each petri dish.1

Which petri dishes had the most bacteria colon
and Kate make based on the data?
We’ll revisit STATS applied! at the end of the chapter, so y
answer these questions.

Starnes_3e_CH01_002-093_v2.indd 3

© 68/Ocean/Corbis

unwanted bacteria? Daniel and Kate de-
al petri dishes, they randomly assigned
ng with soap, 10 students to press one
udents to press one hand in a dish after
counted the number of bacteria colo-
nies? What conclusion did Daniel
you can use what you have learned to help

3

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Lesson 1.1

Statistics: Th
and Art of D

Learning Ta

dd Identify the individuals and v
categorical or quantitative.

dd Summarize the distribution o
frequency table.

We live in a world of data. Every d
studies, and analyses of data on eve
to consumption of bottled water to
To understand what the data are sa

D E F I N I T I O N   Statistics

Statistics is the science and art of co

A solid understanding of stat
data in your daily life.

Activity
The “1 in 6 wins” game

This activity will give you a “taste” of what statistics is a
about: drawing conclusions from data. b
“
As a special promotion for its 20-ounce bottles of 1
soda, a soft-drink company printed a message on the
inside of each bottle cap. Some of the caps said,“Please 2
try again!”while others said,“You’re a winner!” The com-
pany advertised the promotion with the slogan“1 in 6 3
wins a prize.” The prize is a free 20-ounce bottle of soda.
4
Jorge’s statistics class wonders if the company’s
claim holds true at a nearby convenience store. To
find out, all 30 students in the class go to the store,
and each buys one 20-ounce bottle of the soda. Two
of them get caps that say, “You’re a winner!” Does this
result give convincing evidence that the company’s
1-in-6 claim is false? You and your classmates will per-
form a simulation to help answer this question.

For now, let’s assume that the company is telling
the truth and that every 20-ounce bottle of soda it fills
has a 1-in-6 chance of getting a cap that says, “You’re

4

Starnes_3e_CH01_002-093_v2.indd 4

he Science
Data

argets

variables in a data set, then classify the variables as

of a variable with a frequency table or a relative

day, the media report poll results, outcomes of medical
erything from gasoline prices to standardized test scores
o new technology. The data are trying to tell us a story.
aying, you need to learn more about statistics.

ollecting, analyzing, and drawing conclusions from data.

tistics will help you make good decisions based on

a winner!”We can model the status of an individual
bottle with a six-sided die: Let 1 through 5 represent
“Please try again!” and 6 represent “You’re a winner!”
1. Roll your die 30 times to imitate the process of

the students in Jorge’s statistics class buying their
sodas. How many of them won a prize?
2. Your teacher will draw and label axes for a class
dotplot. Plot the number of prize winners you got
in Step 1 on the graph.
3. Have some students repeat Steps 1 and 2 until
you have a total of at least 40 repetitions of the
simulation for your class.
4. Discuss the results with your classmates. What per-
cent of the time did Jorge’s statistics class get two
or fewer prizes, just by chance? Does it seem plau-
sible (believable) that the company is telling the
truth but that the class just got unlucky? Explain.

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LESSO

The previous activity outlines the steps in the st
You’ll learn more about the details of this process in

D E F I N I T I O N   Statistical problem-solving process

•• Ask Questions: Clarify the research problem and ask

questions.

•• Collect Data: Design and carry out an appropriate p
•• Analyze Data: Use appropriate graphical and numer
•• Interpret Results: Draw conclusions based on the d

research question(s)!

Classifying Data

The table displays data on several roller coasters tha

Roller coaster Type Height (ft) Design
Wildfire Wood 187 Sit dow
Skyline Steel 131.3 Inverted
Goliath Wood 165 Sit dow
Helix Steel 134.5 Sit dow
Banshee Steel 167 Inverted
Black Hole Steel 22.7 Sit dow

Most data tables follow this format—each row d

column holds the values of a variable. (Sometimes
called cases or observational units.)

D E F I N I T I O N   Individual, Variable
An individual is a person, animal, or thing described in
A variable is any attribute that can take different values

For the roller coaster data set, the individuals are t
ables recorded for each coaster are: type, height (in
hour), and duration (in seconds). Type and design a
speed, and duration are quantitative variables.

D E F I N I T I O N   Categorical variable, Quantitative v

A categorical variable assigns labels that place individ
A quantitative variable takes number values for which

Not every variable that takes number values is quan
Although zip codes are numbers, it doesn’t make sense
In fact, zip codes place individuals (people or dwellings

Starnes_3e_CH01_002-093_v2.indd 5

O N 1.1  •  Statistics: The Science and Art of Data 5

tatistical problem-solving process.
n future lessons.

s2
k one or more valid statistics

plan to collect the data.
rical methods to analyze the data.
data analysis. Be sure to answer the

at have opened since April 2014.3

n Speed (mph) Duration (s)

wn 70.2 120

d 50 90

wn 72 105

wn 62.1 130

d 68 160

wn 25.5 75

describes an individual and each
the individuals in a data set are

n a set of data.
s for different individuals.

the 6 roller coasters. The five vari-
n feet), design, speed (in miles per
are categorical variables. Height,

variable
duals into particular groups.
h it makes sense to find an average.

ntitative. Zip code is one example. caution
e to talk about the average zip code.
s) into categories based on location. !

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

EXAMPLE

a So you want to be happy?

Individuals and variables

PROBLEM:  The American Statistical Association sponsors a W
about primary and secondary school students using surveys. W
to choose 40 U.S. high school students who completed the sur
displays data for the first 10 students chosen. The rightmost co
question:

Which would you prefer to be? Select one.

______________ Rich ____________ Happy __________

State Grade Gender Birth
level Male Age month
SC Female 17 January
UT 12 Female 14 March
NM 9 Female 17 August
CA 12 Female 17 April
GA 12 Male 17 June
MI 12 Female 17 March
IN 11 Female 18 January
CO 12 Female 14 June
NJ 9 Male 16 November
CO 10 15 January
... 9

Identify the individuals and variables in this data set. Classify ea
q­ uantitative.

SOLUTION:
Individuals: 40 U.S. high school students who completed an online su
Variables:
• Categorical: State where student lives, grade level, gender,

birth month, preferred status
• Quantitative: Age (years), height (centimeters), arm span

(centimeters)

The proper method of data an
or quantitative. For that reason, it
of variables. To make life simpler,
titative data” instead of identifyin

Starnes_3e_CH01_002-093_v2.indd 6

a

Web-based project that collects data
We used the site’s “Random Sampler”
rvey in a recent year.4 The table
olumn gives students’ answers to the

__ Famous ___________ Healthy

Height Arm span Preferred
(cm) (cm) status
177 161 Famous
162 153 Healthy
164 167 Healthy
153 154 Famous
172 169 Happy
170 173 Famous
168 163 Happy
152 160 Happy
165 174 Famous
190 177 Rich

ach variable as categorical or

urvey.

Grade level is a categorical variable even though it takes
number values. The numbers place the students into
categories: 9 = freshman, 10 = sophomore, 11 = junior,
and 12 = senior.

FOR PRACTICE  TRY EXERCISE 1.

nalysis depends on whether a variable is categorical
t is important to distinguish between these two types
, we sometimes refer to “categorical data” or “quan-
ng the variable as categorical or quantitative.

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LESSO

Summarizing Data

A variable generally takes values that vary from one
we call it a variable! The distribution of a variable d
of these values.

D E F I N I T I O N   Distribution
The distribution of a variable tells us what values the v
takes these values.

We can summarize a variable’s distribution with
frequency table.

D E F I N I T I O N   Frequency table, Relative frequenc
A frequency table shows the number of individuals ha
A relative frequency table shows the proportion or pe
data value.

Some people use the terms “frequency distribution
tion” instead. To make either kind of table, start by tal
variable takes each value.

Would you rather be happy or rich?
Frequency and relative frequency tables

PROBLEM:  Here are the data on preferred status for a

Famous Healthy Healthy Famous Happy
Rich Happy Happy Rich Happy
Famous Healthy Rich Happy Happy
Healthy Happy Happy Rich Happy
Famous Happy Happy Happy

Summarize the distribution of preferred status with a

SOLUTION:

Preferred status Tally

Famous |||| ||

Happy ||||  ||||  ||||  |||| |

Healthy ||||

Rich |||| |||

Starnes_3e_CH01_002-093_v2.indd 7

O N 1.1  •  Statistics: The Science and Art of Data 7

individual to another. That’s why
describes the pattern of variation

variable takes and how often it

h a frequency table or a relative

cy table
aving each data value.
ercent of individuals having each

n” and “relative frequency distribu-
llying the number of times that the

EXAMPLE

all 40 students in the sample from the previous example:

Famous Happy Happy Famous
Happy Happy Rich Happy
Rich Happy Happy Rich
Happy Rich Happy Famous

frequency table and a relative frequency table.

Start by tallying the number of students in each
preferred status category.

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

Frequency table

Preferred status Frequency

Famous  7

Happy 21

Healthy  4

Rich  8

Total 40

Relative frequency table

Preferred status Relative frequency

Famous 7/40 = 0.175 or 17.5%

Happy 21/40 = 0.525 or 52.5%

Healthy 4/40 = 0.100 or 10.0%

Rich 8/40 = 0.200 or 20.0%

Total 40/40 5 1.000 or 100%

The same process can be used
able. Of course, it would be hard
table for quantitative data that t
attending a high school band con
variables with many possible valu

l e sso n A pp 1.  1

What are my classmates like?

On the first day of a statistics course, the instructor gave
all 40 students in the class a survey. The table shows data
from the first 10 students on the class roster.

Homework

Pulse Dominant Children last night Sleep

Gender Class GPA rate hand in family (min) (hr)

F Fr 3.22 72 R 3 0–14 10

F Fr 2.3 110 L 3 0–14 8

M Ju 3.8 60 L 6 15–29 7

M So 3.1 72 R 2 15–29 7.5

F So 4.0 51 R 1 45–59 7

F So 3.4 68 R 4 0–14 8.5

F So 3.0 80 R 3 30–44 7

M So 3.5 59 R 2 30–44 7

M Fr 3.9 65 R 2 15–29 6

M Sr 3.5 104 R 2 0–14 7
...

1. Identify the individuals and variables in this
data set. Classify each variable as categorical or
quantitative.

Starnes_3e_CH01_002-093_v2.indd 8

a

The frequency table shows the number of students who
chose each status.

The relative frequency table shows the proportion or
percent of students who chose each status.

FOR PRACTICE  TRY EXERCISE 5.

to summarize the distribution of a quantitative vari-
d to make a frequency table or a relative frequency
take many different values, like the ages of people
ncert. We’ll look at a better option for quantitative
ues in Lesson 1.5.

Have a DGLimages/iStockphoto/Getty Images
smart-
phone? 2. H ere are the ages of the 40 students
in the class:
Y
N 17 16 17 17 17 16 18 14 16 15
Y 16 16 17 18 17 16 17 16 15 14
Y 17 14 14 17 17 17 16 15 17 17
Y 17 18 18 14 15 18 17 17 17 16
Y
Y S ummarize the distribution of age
Y with a frequency table and a relative
Y frequency table.
N

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LESSO

Lesson 1.1

W h a t D i d Yo u L e a r n ?
Learning Target

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

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

Exercises Lesson 1.1

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 Movi
Database, Avatar is tops based on box-office re
pg 6 ceipts worldwide. The table displays data on sev
eral popular movies.5 Identify the individuals an
variables in this data set. Classify each variable a
categorical or quantitative.

Movie Year Rating Time Genre Box office ($)
2009 PG-13 (min) Action 2,783,918,982
Avatar 1997 PG-13 Drama 2,207,615,668
2015 PG-13 162 Adventure 2,040,375,795
Titanic
2015 194 1,669,164,161
Star Wars: 2012 1,519,479,547
The Force 2015 136 1,516,246,709
Awakens 2015 1,404,705,868
PG-13 124 Action
Jurassic 2011 1,328,111,219
World PG-13 142 Action
2013 1,254,512,386
Marvel’s The 2013 PG-13 137 Action 1,172,805,920
Avengers PG-13 141 Action

Furious 7 PG-13 130 Fantasy

The Aveng- PG 108 Animation
ers: Age of PG-13 129 Action
Ultron

Harry Potter
and the
Deathly
Hallows:
Part 2

Frozen

Iron Man 3

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 lis
of available hotels, along with some informatio
about each hotel. The following table displays dat
about hotel options. Identify the individuals an
variables in this data set. Classify each variable a
categorical or quantitative.

Starnes_3e_CH01_002-093_v2.indd 9

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

n classify the Examples Exercises
p. 6 1–4

ncy table or a p. 7 5–8

. Dis-

tance Room

to rate

Exercise Internet Restau- site Room ($/

Hotel Pool room? ($/day) rants (mi) service? day)

ie Comfort Out Y  0 1 8.2 Y 149

e- Inn
v- Fairfield In Y  0 1 8.3 N 119

nd Inn & Y  0 1 3.7 Y 60
as Suites

Baymont Out

Inn &

Suites

Chase Out N 15 0 1.5 N 139
Suite
Hotel

Court- In Y  0 1 0.2 Dinner 114
yard

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 Marital Yearly Travel
of family status income time to
members Age Gender 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

m Pennsylvania 4 44 Male Married $73,000 10
r- Virginia
st 4 22 Male Never $13,000 0
married/

on single
ta California
1 30 Male Never $50,000 15

nd married/
as single

New York 4 34 Female Separated $40,000 40

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

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 Buyer’s Car Engine type Price 8.
name distance model (cylinders)
A
from
Zip dealer 9.
code Gender (mi)
10
P. Smith 27514 M 13 Fiesta 4 $26,375
11
K. Ewing 27510 M 10 Mustang 8 $39,500 12
13
L. Shipman 27516 F 2 Fusion 4 $38,400 14

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
pg 7 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 Telepathy Telepathy Fly Super
strength strength

Invisibility Freeze time Fly Telepathy Freeze time

Telepathy Super Fly Freeze time Telepathy
strength

Freeze Freeze time Freeze time Fly Fly
time

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
July January June November January
December
June December April April January
April
January May December December December
December
August March January July

July April June May

August April October January

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.

Starnes_3e_CH01_002-093_v2.indd 10

a

9 8 6 7.5 7 8 4 7 7 8
88 67 887 768
9 7 6 5 7 8 8.5 7 9 6
6 6.5 8 9 5 8 7 7 7 7
. 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.
3532464435
4422443433
5355444533
3433432624

Applying the Concepts

. 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.

0. 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.

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

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

3. 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.

4. 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.

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Lesson 1.2

Displaying Categor

Learning Targets

dd Make and interpret bar charts of categorical dat
dd Interpret pie charts.
dd Identify what makes some graphs of categorical

A frequency table or relative frequency table sum
with numbers. For instance, the Current Populatio
Census Bureau collected data on the highest educatio
34-year-olds in 2014. The relative frequency table s
the distribution more clearly, use a graph.

Level of education Pe
Less than high school 1
High school graduate 2
Some college 2
Bachelor’s degree 2
Advanced degree 1

You can make a bar chart or a pie chart for c
sometimes called bar graphs. Pie charts are sometim

We’ll discuss graphs for quantitative data in the nex

D E F I N I T I O N   Bar chart, Pie chart

A bar chart shows each category as a bar. The heights o
frequencies or relative frequencies.

A pie chart shows each category as a slice of the “pie.” T
tional to the category frequencies or relative frequencie

Figure 1.1 shows a bar chart and a pie chart
achievement of U.S. 25- to 34-year-olds in 2014. Yo
level of education for this age group was “some coll

Starnes_3e_CH01_002-093_v2.indd 11

rical Data

ta.

l data deceptive.

mmarizes a variable’s distribution
on Survey conducted by the U.S.
onal level achieved by U.S. 25- to
summarizes the data.6 To display

ercent
13.2
22.6
28.7
24.9
10.6

categorical data. (Bar charts are
mes referred to as circle graphs.)
xt few lessons.

of the bars show the category
The areas of the slices are propor-
es.

of the data on the educational
ou can see that the most common
lege.”

11

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Percent 12 C H A P T E R 1   •  Analyzing One -Variable Data

30
25
20
15
10

5
0 Less than High Some Bachelor’

high school college degree
school graduate

(a) Educational level
FIGURE 1.1 (a) Bar chart and (b) pie cha
people aged 25 to 34 in the United State

Bar Charts and Pie Cha

It is fairly easy to make a bar cha

How to Make a Bar Cha

1. Draw and label the axes. Put
horizontal axis. To the left of t
frequency (count) or relative f
category.

2. “Scale” the axes. Write the nam
horizontal axis. On the vertical
you exceed the largest frequen

3. Draw bars above the category
between them. Be sure that the
relative frequency of individua

Making a graph is not an end
stand the data. When you look at

EXAMPLE
a Would students rather be happy or rich?

Making and interpreting a bar chart

PROBLEM:  Here is a frequency table of the
preferred status data for the 40 students in
the “So you want to be happy?” example from
Lesson 1.1. Make a bar chart to display the data.
Describe what you see.

Starnes_3e_CH01_002-093_v2.indd 12

a

Advanced Less than high
degree 10.6% school 13.2%

Bachelor’s High school
degree graduate
24.9% 22.6%

’s Advanced Some college
degree 28.7%

(b)

art of the distribution of educational level attained in 2014 by
es.

arts

art by hand. Here’s how you do it.

art

t the name of the categorical variable under the
the vertical axis, indicate whether the graph shows the
frequency (percent or proportion) of individuals in each

mes of the categories at equally spaced intervals under the
axis, start at 0 and place tick marks at equal intervals until
ncy or relative frequency in any category.
y names. Make the bars equal in width and leave gaps
e height of each bar corresponds to the frequency or
als in that category.

in itself. The purpose of a graph is to help us under-
t a graph, always ask, “What do I see?”

Frequency table

Preferred status Frequency
Famous  7
Happy 21
Healthy  4
Rich  8
Total 40

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Number of students SOLUTION:

Number of students Preferred status
25
Number of students 20
15
10
5
0

Famous Happy Healthy Rich
Preferred status

25
20
15
10

5
0 Famous Happy Healthy Rich

Preferred status

More than half the students (21) said they would rather be
numbers of students chose famous (7) or rich (8) as their p
healthy, chosen by only 4 of the 40 students.

You can use a pie chart when you want to empha
whole. Pie charts are challenging to make by hand, but

Does pie make you happy?
Interpreting pie charts

PROBLEM:  Here is a pie chart of the preferred status
previous example. Explain why the “Famous” slice mak
up 17.5% of the graph.
SOLUTION:
Because the relative frequency for the Famous category is
7/40 5 0.175 or 17.5%.

FOR PRACTICE  TRY

Starnes_3e_CH01_002-093_v2.indd 13

L E S S O N 1.2  •  Displaying Categorical Data 13

1.  Draw and label axes.

2.  “Scale” the axes. The largest frequency is 21. So we
chose a vertical scale from 0 to 25, with tick marks 5 units
apart.

3.  Draw bars.

e happy than famous, healthy, or rich. Similar
preferred status. The least popular status was

FOR PRACTICE  TRY EXERCISE 1.

asize each category’s relation to the EXAMPLE
technology will do the job for you.

Preferred status

data from the Rich Famous
kes 20.0% 17.5%
Y EXERCISE 5.
Healthy
10.0%

Happy
52.5%

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

caution Note that a pie chart must includ
mean adding an “other” category
!

DILBERT © Scott Adams. Used by permission
of UNIVERSAL UCLICK. All rights reserved.

Comparing Distribution Relative frequency

Bar charts and pie charts can dis
can also be used to compare the d
groups. It’s a good idea to use r
comparing, especially if the group

For instance, a random sample
was selected from an international
was recorded along with which su
super strength, telepathy (ability to
The side-by-side bar chart shows
superpower.

40% Fem
35% Mal
30%
25%
20%
15%
10%

5%
0%

Invisib

How do the distributions of
females in the sample? Females we
while males were much more like
males. Females were slightly more
invisibility.

Graphs: Good and Bad

Bar charts are a bit dull to look a
to use special 3-D effects to make
eyes react to the area of the bars
same width, the area (width × hei
receive the right impression about

Starnes_3e_CH01_002-093_v2.indd 14

a

de all categories that make up a whole, which might
y in some settings.

ns with Bar Charts

splay a distribution of categorical data. A bar chart
distribution of a categorical variable in two or more
relative frequencies (percents or proportions) when
ps have different sizes.
e of 200 children ages 9–17 from the United Kingdom
l website’s online survey.7 The gender of each student
uperpower they would most like to have: invisibility,
to read minds), ability to fly, or ability to freeze time.

the percents of males and females who chose each

male
le

bility Super Telepathy Fly Freeze time
strength
Superpower

superpower preference compare for the males and
ere much more likely to choose telepathy than males,
ely to choose super strength or freeze time than fe-
e likely to choose flying and equally likely to choose

at. It is tempting to replace the bars with pictures or
e the graphs seem more interesting. Don’t do it! Our
s as well as to their height. When all bars have the
ight) varies in proportion to the height, and our eyes
t the quantities being compared.

29/03/16 9:09 pm

Who wants to party?

Beware the pictograph!

PROBLEM: The students in a high-school statistics cla
pizza party, or a donut party. Here are the data on the
prefer.

Preferred p
Donut
Pasta
Pizza
Total

(a) Here’s a clever graph of the data that uses pictures
instead of the more traditional bars. How is this
graph misleading?

Frequency 20
18
16 Pasta Pizza
14
12
10

8
6
4
2
0

Donut

Preferred party

SOLUTION:
(a) The pictograph makes it seem like the number of students

who preferred a pizza party (or a donut party) is much
larger than the number of students who preferred a pasta
party, which isn’t the case. The area of the pasta bar is
much smaller than the area of the donut and pizza images.
(b) By starting the vertical scale at 4 instead of 0, it looks
like the number of students who preferred a pizza party is
3 times larger than the number of students who preferred
a donut party, which isn’t the case. In addition, it looks
like the number of students who preferred a pasta party is
more than 4 times larger than the number of students wh
preferred a pizza party, which also is not true.

There are two important lessons to be learned fro
pictograph, and (2) watch those scales.

Starnes_3e_CH01_002-093_v2.indd 15

L E S S O N 1.2  •  Displaying Categorical Data 15

EXAMPLE

ass were recently asked if they would prefer a pasta party, a
e responses of that class about what type of party they would

party Frequency
 5
18
 7
30

(b) Here is a bar chart of the data. Why could this graph
be considered deceptive?

20

18

Frequency 16

14

12

10

8

6

4 Pasta Pizza
Donut

Preferred party

s Although the heights of the pictures are accurate, our
a eyes respond to the area of the pictures.

.

s By starting the vertical scale at a number other than zero,
d we get a distorted impression of the relative numbers of
students in the three categories.

s
ho

FOR PRACTICE  TRY EXERCISE 9.

om this example: (1) beware the caution

!

29/03/16 9:09 pm

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

l e sso n A pp 1.  2
Which cell phone speaks to you?

The Pew Research Center asked a random sample of
2024 adult cell-phone owners from the United States
which type of cell phone they own: iPhone, Android, or
other (including non-smartphones). The frequency table
displays the results.8

Type of cell phone Frequency

iPhone  467

Android  503

Other 1054

Total 2024

1. Make a bar chart to display the distribution of
phone ownership among all 2024 people in the
sample. Describe what you see.

The side-by-side bar chart displays the distri-
bution of phone ownership for each of three age
groups.

2. Write a few sentences comparing the distribu-
tions of phone ownership for the three age
groups.

TCOERCNEHR Making Bar Charts and Pie C

You can use the One Categorical Variable applet at 2
highschool.bfwpub.com/spa3e to make a bar chart or 3
a pie chart. For the preferred-status data (page 12):

Preferred status Frequency
Famous  7
Happy 21
Healthy  4
Rich  8
Total 40

1. Enter Preferred status in the Variable name box.

Starnes_3e_CH01_002-093_v2.indd 16

a

Percent of age group80 18–34
70 35–54
Mel Curtis/Getty Images60 55+

50

40

30

20

10

0 iPhone Android Other

Type of phone

Charts with an Applet

2. Select Single in the Groups menu and choose to
input data as Counts in categories.

3. T ype the category names and frequencies
shown. Click on the + button to add rows to
the frequency table.

29/03/16 9:09 pm

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

Lesson 1.2

W h a t D i d Yo u L e a r n ?
Learning Target

Make and interpret bar charts of categorical data.
Interpret pie charts.
Identify what makes some graphs of categorical data d

Exercises Lesson 1.2

Mastering Concepts and Skills

1. Radio frequencies? Arbitron, the rating service for ra
dio audiences, places U.S. radio stations into catego
pg 12 ries that describe the kinds of programs they broad
cast. The frequency table summarizes the distributio
of station formats in a recent year.9 Make a bar char
to display the data. Describe what you see.

Format Count of stations

Adult contemporary 2536
All sports 1274
Contemporary hits 1012
Country 2893
News/talk/information 4077
Oldies  831
Religious 3884
Rock 1636
Spanish language  878
Variety 1579
Other formats 4852

Starnes_3e_CH01_002-093_v2.indd 17

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

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

deceptive. Examples Exercises
p. 12 1–4
p. 13 5–8
p. 15 9–12

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

29/03/16 9:09 pm

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

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

Color Percent of vehicles S
Black 19 la
Blue 6
Brown/beige 5 6.
Gray 12
Green 1 7.
Red 9
Silver 14
White 29
Yellow/gold 3
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
Internet. Here is a relative frequency table that
summarizes data on the most common types of
spam.11

Type of spam Percent
Adult 19
Financial 20
Health 7
Internet 7
Leisure 6
Products 25
Scams 9
Other ??

(a) What percent of spam would fall in the “Other” cat-
egory?

(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 At top right is a pie chart of the
radio station format data from Exercise 1. What
pg 13 percent of the graph does the “Country” slice make
up? Justify your answer.

Starnes_3e_CH01_002-093_v2.indd 18

a

Adult
contemporary

Other All sports Contemporary
formats hit

Spanish Variety Country
anguage
Rock
Religious News/Talk/
Info

Oldies

. 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.

Saturday Sunday

Friday Monday

Thursday Tuesday

Wednesday

. 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?

Technical
Arts/Humanities
Other Bioslcoigeinccael s
Business
Professional
Social Education
sciences Engineering

Physical sciences

29/03/16 9:09 pm

8. Family origins Here is a pie chart of Census Burea
data to show the countries from which the mor
than 14 million Asians in the United States in 201
descend.13 About what percent of Asians were o
Chinese origin? Korean?

Other Asian Chinese
Japanese

Korean Indian

Vietnamese
Filipino

9. Game on! Students in a high school statistic
class were given data about the favorite sport t
pg 15 play for a group of 35 girls. They produced th
following pictograph. Explain how this graph i
misleading.

Sports Tennis Key:
Soccer = 4 Players
Softball = 5 Players
Basketball
= 2 Players

= 2 Players

10. Social media The Pew Research Center surveye
a random sample of U.S. teens and adults abou
their use of social media in 2013. The followin
pictograph displays some results. Explain how thi
graph is misleading.

AGE BREAKDOWN (OF SOCIAL MEDIA USERS)
13 –18 19–29 30 – 49 50 – 64 65 +

89%
81%

78% 43%
60%

11. Support the court? A news network reported th
results of a survey about a controversial cour
decision. The network initially posted on its websit
a bar chart of the data similar to the one that follow

Starnes_3e_CH01_002-093_v2.indd 19

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

au Explain how this graph is misleading. (Note: WhenPercent who agree
re notified about the misleading nature of its graph,
10 the network posted a corrected version.)
of 63

62
61
60
59
58
57
56
55
54
53

Democrats 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-
cs leading.
to
he 280
is 260
Number of students
240

220

200

180

160

140

120

100
Math Science English Social Foreign Fine
studies language arts

Favorite subject

ed Applying the Concepts
ut
ng 13. Frequent superpower? The online survey from
is ­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 Telepathy Telepathy Fly Super
strength strength

Invisibility Freeze time Fly Telepathy Freeze time

Telepathy Super Fly Freeze Telepathy
strength time

Freeze time Freeze time Freeze time Fly Fly

he Fly Freeze time Invisibility Fly Invisibility
rt
te Telepathy Telepathy Fly Telepathy Fly

ws. Fly Telepathy Telepathy Fly Fly

29/03/16 9:09 pm

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

14. Birth months Here are the reported birth months Ex
for the 40 students in the online sample. Make a
relative frequency bar chart for these data from 17
Lesson 1.1 (page 6). Describe what you see.
18
January March August April June
March January June November January (a
July December April April January (b
December May December December December
June August March January July R
April July April June May
January August April October January 19
December March February July June
B
15. Far from home A survey asked first-year college B
students, “How many miles is this college from your
permanent home?” Students had to choose from S
the following options: 5 or fewer, 6 to 10, 11 to 50, M
51 to 100, 101 to 500, or more than 500. The bar C
chart shows the percentage of students at public and H
private 4-year colleges who chose each option.14 O
Write a few sentences comparing the distributions C
of distance from home for students from private and T
public 4-year colleges who completed the survey. S
F
35 Public In
30 Private C
C
25 P
Z
Percent 20 W
T
15

10

5

0
5 or 6 to 10 11 to 51 to 101 to More

fewer 50 100 500 than

500

Distance from home (miles)

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
U.S.

25 Europe

20

Percent 15

10

5

0 White/ Black Silver Blue Gray Red Beige/ Green Yellow/

pearl brown gold

Color

Starnes_3e_CH01_002-093_v2.indd 20

a

xtending the Concepts

7. 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?

8. 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

Percent who attended a movie80
70
60
50
40
30
20
10

0 18–24 25–34 35–44 45–54 55–64 65–74 75
and older

Age group (years)

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

9. 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 Country Height Floors Use Year
(m) 163 Mixed completed
Burj Khalifa United 828
Arab 121 Mixed 2010
­Emirates 632 120 Hotel
601 2014
Shanghai Tower China 104 Office 2012
541 101 Office
Makkah Royal Saudi 101 Mixed 2013
Clock Tower Arabia 509 118 Mixed
Hotel 492 2004
88 Office 2008
One World Trade United 484 89 Mixed
108 Office 2010
Center States 452
450 1998
Taipei 101 Taiwan 442 2010
1974
Shanghai World China
Financial Center

nternational China
Commerce
Center

Petronas Tower 1 Malaysia

Zifeng Tower China

Willis (Sears) United
Tower States

29/03/16 9:09 pm

Lesson 1.3

Displaying Quantit
Dotplots

Learning Targets

dd Make and interpret dotplots of quantitative data
dd Describe the shape of a distribution.
dd Compare distributions of quantitative data with

You can use a bar chart or pie chart to display categ
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 loca

Figure 1.2 shows a dotplot of the number of sibli
statistics class. You’ll learn how to make and interpr

d
d
dd
dd
dd
dd
dd
dd
dd
dd
dd
dddd
dddd
d d ddd
d d dddd

01234
Number of siblings

Making and Interpreting Dotplots

For small sets of quantitative data, it is fairly easy to

How to Make a Dotplot

1. Draw and label the axis. Draw a horizontal axis and
variable underneath.

2. Scale the axis. Find the smallest and largest values i
axis at a number equal to or less than the smallest va
intervals until you equal or exceed the largest value.

3. Plot the values. Mark a dot above the location on th
each data value. Try to make all the dots the same siz
stack them.

Remember what we said in Lesson 1.2: Making
When you look at a graph, always ask, “What do I s

Starnes_3e_CH01_002-093_v2.indd 21

tative Data:

a.
h dotplots.
gorical data. A dotplot is the sim-

ation on a number line.

ings reported by each student in a FIGURE 1.2 Dotplot of
ret dotplots in this lesson. data on the number of
siblings reported by stu-
dd dents in a statistics class.

567

make a dotplot by hand.

d put the name of the quantitative

in the data set. Start the horizontal
alue and place tick marks at equal
.
he horizontal axis corresponding to
ze and space them out equally as you

g a graph is not an end in itself.
see?”

21

29/03/16 9:09 pm

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

EXAMPLE
a Which cars guzzle gas? 

Making a dotplot

PROBLEM:  The Environmental Protection Agency (EPA) is in
charge of determining and reporting fuel economy ratings for
cars. Think of those large window stickers on a new car. Here
are the EPA estimates of highway gas mileage in miles per
gallon (mpg) for a sample of 21 model year 2014 midsize cars.1

Model mpg Model m

Acura RLX 31 Dodge Avenger

Audi A8 28 Ford Fusion

BMW 550i 25 Hyundai Elantra

Buick Lacrosse 28 Jaguar XF

Cadillac CTS 27 Kia Optima

Chevrolet Malibu 30 Lexus ES 350

Chrysler 200 30 Lincoln MKZ

(a) Make a dotplot of these data.
(b) Explain what the dot above 38 represents.
(c) What percent of the car models in the sample get more th

SOLUTION:

(a)

Highway gas mileage (mpg)

25 30 35 40 45 50
Highway gas mileage (mpg)

dd dd d dd d
dd dd dd
dd 50
25 dd
d dd

30 35 40 45

Highway gas mileage (mpg)

(b) The dot above 38 represents the 2014 Hyundai Elantra,
which gets 38 mpg on the highway.

(c) 3/21 ≈ 0.143 or about 14.3% of the car models in the
sample get more than 35 mpg on the highway.

FOR PRACTICE  TRY EXERCISE 1.

Starnes_3e_CH01_002-093_v2.indd 22

a

17 © D. Hurst/Alamy Stock Photo

mpg Model mpg

30 Mazda 6 40

31 Mercedes-Benz E350 30

38 Nissan Maxima 26

30 Subaru Legacy 32

31 Toyota Prius 48

31 Volkswagen Passat 34

31 Volvo S80 25

han 35 mpg on the highway?

1.  Draw and label the axis.

2.  Scale the axis. The smallest value is 25 and the
largest value is 48. So we chose a scale from 25 to 50 with
tick marks 5 units apart.
3.  Plot the values.

dd dd d dd d
dd dd dd
dd 50
dd
d dd

25 30 35 40 45

Highway gas mileage (mpg)

29/03/16 9:09 pm

LESSON

Describing Shape

When you describe the shape of a dotplot or other
on the main features. Look for major peaks, not f
graph. Look for clusters of values and obvious ga
roughly symmetric or clearly skewed.

D E F I N I T I O N   Symmetric and skewed distribution

A distribution is roughly symmetric if the right side of t
the observations with larger values) is approximately a

d d
dd d
dd dd
ddd
ddd
ddd
ddd
ddd

Roughly symmetric

A distribution is skewed to the right if the right side of
the left side.

d
d
d
dd
ddd
dd dd
dd ddd
dd ddd
dd ddd

Skewed to the right

A distribution is skewed to the left if the left side of t
right side.

d
d
d
d
dd
dd
d dd
dd dd
ddd dd

Skewed to the left

Forease,wesometimes say“left-skewed”instead of“ske
instead of “skewed to the right.” The direction of ske
the direction where most observations are clustered.
corny way to help you keep this straight. To avoid dan
slope—in the direction of the skewness.

Skewed
to the
left!

Starnes_3e_CH01_002-093_v2.indd 23

N 1.3  •  Displaying Quantitative Data: Dotplots 23

graph of quantitative data, focus
for minor ups and downs in the
aps. Decide if the distribution is

ns
the graph (containing the half of
mirror image of the left side.

d
d
dd
dd

f the graph is much longer than

d
dd

the graph is much longer than the

d
d
dd
dd
dd
dd

ewed to theleft”and“right-skewed” caution
ewness is toward the long tail, not
The drawing below is a cute but !
nger, Mr. Starnes skis on the gentler

29/03/16 9:09 pm

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

EXAMPLE

a What do distributions show?

Describing shape

PROBLEM:  The dotplots below display two differ-
ent sets of quantitative data. Graph (a) shows the EPA
highway gas mileage ratings for a sample of 21 model
year 2014 midsize cars. Graph (b) shows the results of
100 rolls of a 6-sided die. Describe the shape of each
distribution.

dd dd d dd d
dd dd dd
dd 50
25 dd
d dd
(a)
30 35 40 45

Highway gas mileage (mpg) (b

SOLUTION:
(a) The dotplot is right-skewed with a single peak near 30

to 31 mpg, one main cluster of dots between 25 and 34
mpg, a small gap from 34 to 38 mpg, and a large gap from
40 to 48 mpg.
(b) The distribution of die rolls is roughly symmetric with no clear
peak. It has about the same height for all values from 1 to 6.

FIGURE 1.3  Dotplot dis- Some quantitative variables hav
playing the duration, in distributions have irregular shapes
minutes, of 220 eruptions show other patterns, like the two d
of the Old Faithful geyser. examine a graph of quantitative da
This distribution has two
main clusters of data and dd
two clear peaks—one dd
near 2 minutes and the dd ddd
other near 4.5 minutes. dd dd d
We could describe this dd dd dd
graph as bimodal be- dd d
cause it has two peaks. dd dd dd dd
dd dd dd dd
ddd ddd ddd ddd ddd ddd
d dd dd dd dd dd dd
dd dd dd dd dd dd dd d
dddddddd d
dd dd dd dd dd dd dd dd dd dd dd

1.5 2.0 2.5

Describing and Compa

Here is a general strategy for desc

Starnes_3e_CH01_002-093_v2.indd 24

a

d

ddd

ddd

d d dd

ddd dd

dddddd

dddddd

dddddd

dddddd

dddddd

dddddd

dddddd

dddddd

dddddd

dddddd

dddddd

dddddd

dddddd

dddddd

123456

b) Roll

We can describe the shape of the distribution of die rolls
as “approximately uniform.”

FOR PRACTICE  TRY EXERCISE 7.

ve distributions with easily described shapes. But many
s that are neither symmetric nor skewed. Some data
distinct clusters and two peaks in Figure 1.3. When you
ata, describe any pattern you see as clearly as you can.

d
ddd
dd
dd
ddd
d d dd
dd dd dd
ddd ddd d
dd
dd dd dd
dd dd ddd
dd d d d
dd d
dd dd dd dd dd dd
dd dd d dd dd dd dd
ddd ddd ddd ddd ddd ddd ddd
dd dd dd dd dd dd dd
d dd dd dd dd dd dd dd dd dd d
dd d d dddddddddddd
dd dd dd d d d dd d d dd dd dd dd dd dd dd dd dd dd dd dd d d

5 3.0 3.5 4.0 4.5 5.0

Duration (min)

aring Distributions

cribing a distribution of quantitative data.

29/03/16 9:09 pm

LESSON

How to Describe the Distribution of a

In any graph, look for the overall pattern and for clear dep
• You can describe the overall pattern of a distribution
• An important kind of departure is an outlier, a value

We will discuss more formal ways to measur
identify outliers in future lessons. For now, just us
these ideas in previous math courses when desc
quantitative data.

Anybody home?
Comparing distributions with dotplots

PROBLEM: How do the numbers of people living in h
South Africa compare? To help answer this question, w
Selector” to choose 50 students from each country. He
sizes reported by the survey respondents. Compare th
two countries.

South Africa d
d
d d d
d
d 25 30
d
d
d
dd
ddddd
dddddd
ddddddd d
dddddddd d
dddddddddd

0 5 10 15 20
Household size

SOLUTION:

Shape:  The South Africa distribution is skewed to the right a
roughly symmetric and single-peaked.
Center:  Household sizes for the South African students tend
(center ≈ 4).
Variability:  The household sizes for the South African stude
U.K. students (from 2 to 6 people).
Outliers:  There aren’t any obvious outliers in the U.K. dotplo
dotplot—students living in households with 15 and 26 people

Starnes_3e_CH01_002-093_v2.indd 25

N 1.3  •  Displaying Quantitative Data: Dotplots 25

Quantitative Variable

partures from that pattern.
n by its shape, center, and variability.
e that falls outside the overall pattern.

re center and variability and to
se what you have learned about
cribing or comparing graphs of

EXAMPLE

U.K.households in the United Kingdom (U.K.) and
we used Census At School’s “Random Data
ere are parallel dotplots of the household
he distributions of household size for these

d
d
d
d
d
d
dd
dd
dd
dd
dd
dd
dd
dd
dd
ddd
dddd
dddd
ddddd
ddddd
ddddd

0 5 10 15 20 25 30
Household size

and single-peaked, while the U.K. distribution is

d to be larger (center ≈ 6) than for the U.K. students

ents vary more (from 3 to 26 people) than for the

ot. The two large values in the South Africa
e—appear to be outliers.

FOR PRACTICE  TRY EXERCISE 11.

29/03/16 9:09 pm

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

When comparing distribution
values for the center and variab
compare these values, using expr
the same as.”

l e sso n A pp 1.  3
How can we check the health of a stream?

Nitrates are organic compounds that are a main
ingredient in fertilizers. When those fertilizers run off
into streams, the nitrates can have a toxic effect on
fish. An ecologist studying nitrate pollution in two
streams measures nitrate concentrations at 42 places
on Stony Brook and 42 places on Mill Brook. The
parallel dotplots display the data.

d

d dd

d d dd d d 2.

d ddd dd dd dd d 3.
4.
Stony Brook d dddddddddddddddddd dd
d

ddd

dd d dd d dd d d

Mill Brook d dd dddddddddddddddddd dd ddd dd

0 2 4 6 8 10 12 14 16 18 20

Nitrate concentration (mg/l)

1. Explain what the dot above 12 in the Stony Brook
graph represents.

TCOERCNEHR Making a Dotplot Using an A

You can use the One Quantitative Variable applet at
highschool.bfwpub.com/spa3e to make a dotplot.
For the highway gas mileage data on page 22:

1. Enter Highway gas mileage as the Variable
name.

T
fo
m
S

Starnes_3e_CH01_002-093_v2.indd 26