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The basic practice of statistics 3rd Edition David S.
Moore Digital Instant Download
Author(s): David S. Moore
ISBN(s): 9780716796237, 0716796236
Edition: 3rd
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Year: 2003
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Exploring Data
T
he first step in understanding data is to hear what the data say, to “let
the statistics speak for themselves.” But numbers speak clearly only
when we help them speak by organizing, displaying, summarizing, and
asking questions. That’s data analysis. The six chapters in Part I present the
ideas and tools of statistical data analysis. They equip you with skills that are
immediately useful whenever you deal with numbers.
These chapters reflect the strong emphasis on exploring data that character-
izes modern statistics. Although careful exploration of data is essential if we are
to trust the results of inference, data analysis isn’t just preparation for inference.
To think about inference, we carefully distinguish between the data we actually
have and the larger universe we want conclusions about. The Bureau of Labor
Statistics, for example, has data about employment in the 55,000 households
contacted by its Current Population Survey. The bureau wants to draw conclu-
sions about employment in all 110 million U.S. households. That’s a complex
problem. From the viewpoint of data analysis, things are simpler. We want to
explore and understand only the data in hand. The distinctions that inference
requires don’t concern us in Chapters 1 to 6. What does concern us is a sys-
tematic strategy for examining data and the tools that we use to carry out that
strategy.
Part of that strategy is to first look at one thing at a time and then at relation-
ships. In Chapters 1, 2, and 3 you will study variables and their distributions.
Chapters 4, 5, and 6 concern relationships among variables.
0

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PART
I
EXPLORING DATA: VARIABLES AND DISTRIBUTIONS
Chapter 1 Picturing Distributions with Graphs
Chapter 2 Describing Distributions with Numbers
Chapter 3 The Normal Distributions
EXPLORING DATA: RELATIONSHIPS
Chapter 4 Scatterplots and Correlation
Chapter 5 Regression
Chapter 6 Two-Way Tables
EXPLORING DATA REVIEW
1

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2

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CHAPTER
1
(Darrell
Ingham/Allsport
Concepts/Getty
Images)
Picturing Distributions
with Graphs
Inthischapterwecover...
Individuals and variables
Categorical variables:
pie charts and bar graphs
Quantitative variables:
histograms
Interpreting histograms
Quantitative variables:
stemplots
Time plots
Statistics is the science of data. The volume of data available to us is over-
whelming. Each March, for example, the Census Bureau collects economic and
employment data from more than 200,000 people. From the bureau’s Web site
you can choose to examine more than 300 items of data for each person (and
more for households): child care assistance, child care support, hours worked,
usual weekly earnings, and much more. The first step in dealing with such a
flood of data is to organize our thinking about data.
Any set of data contains information about some group of individuals. The in-
formation is organized in variables.
INDIVIDUALS AND VARIABLES
Individuals are the objects described by a set of data. Individuals may be
people, but they may also be animals or things.
A variable is any characteristic of an individual. A variable can take
different values for different individuals.
3

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4 CHAPTER 1 r Picturing Distributions with Graphs
A college’s student data base, for example, includes data about every cur-
rently enrolled student. The students are the individuals described by the data
set. For each individual, the data contain the values of variables such as date
of birth, gender (female or male), choice of major, and grade point average. In
practice, any set of data is accompanied by background information that helps
us understand the data. When you plan a statistical study or explore data from
someone else’s work, ask yourself the following questions:
Are data artistic?
David Galenson, an economist
at the University of Chicago,
uses data and statistical
analysis to study innovation
among painters from the
nineteenth century to the
present. Economics journals
publish his work. Art history
journals send it back
unread.“Fundamentally
antagonistic to the way
humanists do their work,”said
the chair of art history at
Chicago. If you are a student of
the humanities, reading this
statistics text may help you
start a new wave in your field.
1. Who? What individuals do the data describe? How many individuals
appear in the data?
2. What? How many variables do the data contain? What are the exact
definitions of these variables? In what units of measurement is each
variable recorded? Weights, for example, might be recorded in pounds,
in thousands of pounds, or in kilograms.
3. Why? What purpose do the data have? Do we hope to answer some
specific questions? Do we want to draw conclusions about individuals
other than the ones we actually have data for? Are the variables suitable
for the intended purpose?
Some variables, like gender and college major, simply place individuals into
categories. Others, like height and grade point average, take numerical values
for which we can do arithmetic. It makes sense to give an average income for a
company’s employees, but it does not make sense to give an “average” gender.
We can, however, count the numbers of female and male employees and do
arithmetic with these counts.
CATEGORICAL AND QUANTITATIVE VARIABLES
A categorical variable places an individual into one of several groups or
categories.
A quantitative variable takes numerical values for which arithmetic
operations such as adding and averaging make sense.
The distribution of a variable tells us what values it takes and how often
it takes these values.
EXAMPLE 1.1 A professor’s data set
Here is part of the data set in which a professor records information about student
performance in a course:

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5
The individuals described are the students. Each row records data on one individual.
Each column contains the values of one variable for all the individuals. In addition
to the student’s name, there are 7 variables. School and major are categorical vari-
ables. Scores on homework, the midterm, and the final exam and the total score
are quantitative. Grade is recorded as a category (A, B, and so on), but each grade
also corresponds to a quantitative score (A = 4, B = 3, and so on) that is used to
calculate student grade point averages.
Most data tables follow this format—each row is an individual, and each col-
umn is a variable. This data set appears in a spreadsheet program that has rows and spreadsheet
columns ready for your use. Spreadsheets are commonly used to enter and transmit
data and to do simple calculations such as adding homework, midterm, and final
scores to get total points.
APPLY YOUR KNOWLEDGE
1.1 Fuel economy. Here is a small part of a data set that describes the fuel
economy (in miles per gallon) of 2002 model motor vehicles:
Make and Vehicle Transmission Number of City Highway
model type type cylinders MPG MPG
·
·
·
Acura NSX Two-seater Automatic 6 17 24
Audi A4 Compact Manual 4 22 31
Buick Century Midsize Automatic 6 20 29
Dodge Ram 1500 Standard pickup truck Automatic 8 15 20
·
·
·
(a) What are the individuals in this data set?
(b) For each individual, what variables are given? Which of these
variables are categorical and which are quantitative?
1.2 A medical study. Data from a medical study contain values of many
variables for each of the people who were the subjects of the study.
Which of the following variables are categorical and which are
quantitative?
(a) Gender (female or male)
(b) Age (years)
(c) Race (Asian, black, white, or other)
(d) Smoker (yes or no)
(e) Systolic blood pressure (millimeters of mercury)
(f) Level of calcium in the blood (micrograms per milliliter)

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Categorical variables: pie charts and bar graphs
Statistical tools and ideas help us examine data in order to describe their main
features. This examination is called exploratory data analysis. Like an explorer
exploratory data analysis
crossing unknown lands, we want first to simply describe what we see. Here are
two basic strategies that help us organize our exploration of a set of data:
r Begin by examining each variable by itself. Then move on to study the
relationships among the variables.
r Begin with a graph or graphs. Then add numerical summaries of specific
aspects of the data.
We will follow these principles in organizing our learning. Chapters 1 to 3
present methods for describing a single variable. We study relationships among
several variables in Chapters 4 to 6. In each case, we begin with graphical dis-
plays, then add numerical summaries for more complete description.
The proper choice of graph depends on the nature of the variable. The val-
ues of a categorical variable are labels for the categories, such as “male” and
“female.” The distribution of a categorical variable lists the categories and
gives either the count or the percent of individuals who fall in each category.
EXAMPLE 1.2 Garbage
The formal name for garbage is “municipal solid waste.”Here is a breakdown of the
materials that made up American municipal solid waste in 2000.1
Weight
Material (million tons) Percent of total
Food scraps 25.9 11.2%
Glass 12.8 5.5%
Metals 18.0 7.8%
Paper, paperboard 86.7 37.4%
Plastics 24.7 10.7%
Rubber, leather, textiles 15.8 6.8%
Wood 12.7 5.5%
Yard trimmings 27.7 11.9%
Other 7.5 3.2%
Total 231.9 100.0
It’s a good idea to check data for consistency. The weights of the nine materials
add to 231.8 million tons, not exactly equal to the total of 231.9 million tons given
in the table. What happened? Roundoff error: Each entry is rounded to the nearest
roundoff error
tenth, and the total is rounded separately. The exact values would add exactly, but
the rounded values don’t quite.
The pie chart in Figure 1.1 shows us each material as a part of the whole.
pie chart
For example, the “plastics” slice makes up 10.7% of the pie because 10.7% of
municipal solid waste consists of plastics. The graph shows more clearly than
the numbers the predominance of paper and the importance of food scraps,

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7
Categorical variables: pie charts and bar graphs
Food scraps
Glass
Metals
Paper
Plastics
Rubber, leather, textiles
Wood
Yard trimmings
Other
Figure 1.1 Pie chart of
materials in municipal solid
waste, by weight.
plastics, and yard trimmings in our garbage. Pie charts are awkward to make by
hand, but software will do the job for you.
We could also make a bar graph that represents each material’s weight by bar graph
the height of a bar. To make a pie chart, you must include all the categories
that make up a whole. Bar graphs are more flexible. Figure 1.2(a) is a bar graph
of the percent of each material that was recycled or composted in 2000. These
percents are not part of a whole because each refers to a different material. We
could replace the pie chart in Figure 1.1 by a bar graph, but we can’t make a pie
chart to replace Figure 1.2(a). We can often improve a bar graph by changing
the order of the groups we are comparing. Figure 1.2(b) displays the recycling
data with the materials in order of percent recycled or composted. Figures 1.1
and 1.2 together suggest that we might pay more attention to recycling plastics.
Bar graphs and pie charts help an audience grasp the distribution quickly.
They are, however, of limited use for data analysis because it is easy to under-
stand data on a single categorical variable without a graph. We will move on
to quantitative variables, where graphs are essential tools.
1.3 The color of your car. Here is a breakdown of the most popular colors
for vehicles made in North America during the 2001 model year:2
Color Percent Color Percent
Silver 21.0% Medium red 6.9%
White 15.6% Brown 5.6%
Black 11.2% Gold 4.5%
Blue 9.9% Bright red 4.3%
Green 7.6% Grey 2.0%
(a) What percent of vehicles are some other color?
(b) Make a bar graph of the color data. Would it be correct to make a
pie chart if you added an “Other”category?

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Yard Paper Metals Glass Textiles Other Plastics Wood Food
0
10
20
30
40
60
50
Material
Percent
recycled
(b)
Food Glass Metals Paper Plastics Textiles Wood Yard Other
0
10
20
30
40
50
60
(a)
Percent
recycled
Material
The height of this bar is 45.4
because 45.4% of paper
municipal waste was recycled.
Figure 1.2 Bar graphs comparing the percents of each material in municipal solid
waste that were recycled or composted.

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9
Quantitative variables: histograms
1.4 Never on Sunday? Births are not, as you might think, evenly
distributed across the days of the week. Here are the average numbers of
babies born on each day of the week in 1999:3
Day Births
Sunday 7,731
Monday 11,018
Tuesday 12,424
Wednesday 12,183
Thursday 11,893
Friday 12,012
Saturday 8,654
Present these data in a well-labeled bar graph. Would it also be correct
to make a pie chart? Suggest some possible reasons why there are fewer
births on weekends.
Quantitative variables: histograms
Quantitative variables often take many values. A graph of the distribution is
clearer if nearby values are grouped together. The most common graph of the
distribution of one quantitative variable is a histogram. histogram
EXAMPLE 1.3 Making a histogram
One of the most striking findings of the 2000 census was the growth of the His-
panic population of the United States. Table 1.1 presents the percent of resi-
dents in each of the 50 states who identified themselves in the 2000 census as
“Spanish/Hispanic/Latino.”4
The individuals in this data set are the 50 states. The
variable is the percent of Hispanics in a state’s population. To make a histogram of
the distribution of this variable, proceed as follows:
Step 1. Choose the classes. Divide the range of the data into classes of equal
width. The data in Table 1.1 range from 0.7 to 42.1, so we decide to
choose these classes:
0.0 ≤ percent Hispanic < 5.0
·
·
·
Be sure to specify the classes precisely so that each individual falls into
exactly one class. A state with 4.9% Hispanic residents would fall into
the first class, but a state with 5.0% falls into the second.

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TABLE 1.1 Percent of population of Hispanic origin, by state (2000)
State Percent State Percent State Percent
Alabama 1.5 Louisiana 2.4 Ohio 1.9
Alaska 4.1 Maine 0.7 Oklahoma 5.2
Arizona 25.3 Maryland 4.3 Oregon 8.0
Arkansas 2.8 Massachusetts 6.8 Pennsylvania 3.2
California 32.4 Michigan 3.3 Rhode Island 8.7
Colorado 17.1 Minnesota 2.9 South Carolina 2.4
Connecticut 9.4 Mississippi 1.3 South Dakota 1.4
Delaware 4.8 Missouri 2.1 Tennessee 2.0
Florida 16.8 Montana 2.0 Texas 32.0
Georgia 5.3 Nebraska 5.5 Utah 9.0
Hawaii 7.2 Nevada 19.7 Vermont 0.9
Idaho 7.9 New Hampshire 1.7 Virginia 4.7
Illinois 10.7 New Jersey 13.3 Washington 7.2
Indiana 3.5 New Mexico 42.1 West Virginia 0.7
Iowa 2.8 New York 15.1 Wisconsin 3.6
Kansas 7.0 North Carolina 4.7 Wyoming 6.4
Kentucky 1.5 North Dakota 1.2
Step 2. Count the individuals in each class. Here are the counts:
Class Count Class Count Class Count
0.0 to 4.9 27 15.0 to 19.9 4 30.0 to 34.9 2
5.0 to 9.9 13 20.0 to 24.9 0 35.0 to 39.9 0
10.0 to 14.9 2 25.0 to 29.9 1 40.0 to 44.9 1
Step 3. Draw the histogram. Mark the scale for the variable whose distribution
you are displaying on the horizontal axis. That’s the percent of a state’s
population who are Hispanic. The scale runs from 0 to 45 because that
is the span of the classes we chose. The vertical axis contains the scale
of counts. Each bar represents a class. The base of the bar covers the
class, and the bar height is the class count. There is no horizontal space
between the bars unless a class is empty, so that its bar has height zero.
Figure 1.3 is our histogram.
The bars of a histogram should cover the entire range of values of a vari-
able. When the possible values of a variable have gaps between them, extend
the bases of the bars to meet halfway between two adjacent possible values.
For example, in a histogram of the ages in years of university faculty, the bars
representing 25 to 29 years and 30 to 34 years would meet at 29.5.
Our eyes respond to the area of the bars in a histogram.5
Because the classes
are all the same width, area is determined by height and all classes are fairly
represented. There is no one right choice of the classes in a histogram. Too

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11
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40 45
Percent Hispanic
Number
of
states
New Mexico, 42.1% Hispanic,
may be a high outlier.
The height of this bar is 13
because 13 states had between
5.0% and 9.9% Hispanic
residents.
Figure 1.3 Histogram of the distribution of the percent of Hispanics among the
residents of the 50 states. This distribution is skewed to the right.
few classes will give a “skyscraper” graph, with all values in a few classes with
tall bars. Too many will produce a “pancake” graph, with most classes having
one or no observations. Neither choice will give a good picture of the shape of
the distribution. You must use your judgment in choosing classes to display the
shape. Statistics software will choose the classes for you. The software’s choice
is usually a good one, but you can change it if you want.
1.5 Sports car fuel economy. Interested in a sports car? The Environmental
Protection Agency lists most such vehicles in its “two-seater”category.
Table 1.2 gives the city and highway mileages (miles per gallon) for the
22 two-seaters listed for the 2002 model year.6
Make a histogram of the
highway mileages of these cars using classes with width 5 miles per
gallon.
Making a statistical graph is not an end in itself. The purpose of the graph is to
help us understand the data. After you make a graph, always ask, “What do I
see?”Once you have displayed a distribution, you can see its important features
as follows.

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TABLE 1.2 Gas mileage (miles per gallon) for 2002 model two-seater cars
Model City Highway Model City Highway
Acura NSX 17 24 Honda Insight 57 56
Audi TT Quattro 20 28 Honda S2000 20 26
Audi TT Roadster 22 31 Lamborghini Murcielago 9 13
BMW M Coupe 17 25 Mazda Miata 22 28
BMW Z3 Coupe 19 27 Mercedes-Benz SL500 16 23
BMW Z3 Roadster 20 27 Mercedes-Benz SL600 13 19
BMW Z8 13 21 Mercedes-Benz SLK230 23 30
Chevrolet Corvette 18 25 Mercedes-Benz SLK320 20 26
Chrysler Prowler 18 23 Porsche 911 GT2 15 22
Ferrari 360 Modena 11 16 Porsche Boxster 19 27
Ford Thunderbird 17 23 Toyota MR2 25 30
EXAMINING A DISTRIBUTION
In any graph of data, look for the overall pattern and for striking
deviations from that pattern.
You can describe the overall pattern of a histogram by its shape, center,
and spread.
An important kind of deviation is an outlier, an individual value that
falls outside the overall pattern.
We will learn how to describe center and spread numerically in Chapter 2.
For now, we can describe the center of a distribution by its midpoint, the value
with roughly half the observations taking smaller values and half taking larger
values. We can describe the spread of a distribution by giving the smallest and
largest values.
EXAMPLE 1.4 Describing a distribution
Look again at the histogram in Figure 1.3. Shape: The distribution has a single peak,
which represents states that are less than 5% Hispanic. The distribution is skewed to
the right. Most states have no more than 10% Hispanics, but some states have much
higher percentages, so that the graph trails off to the right. Center: Table 1.1 shows
that about half the states have less than 4.7% Hispanics among their residents and
half have more. So the midpoint of the distribution is close to 4.7%. Spread: The
spread is from about 0% to 42%, but only four states fall above 20%.
Outliers: Arizona, California, New Mexico, and Texas stand out. Whether these
are outliers or just part of the long right tail of the distribution is a matter of judg-
ment. There is no rule for calling an observation an outlier. Once you have spotted
possible outliers, look for an explanation. Some outliers are due to mistakes, such
as typing 4.2 as 42. Other outliers point to the special nature of some observations.
These four states are heavily Hispanic by history and location.

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13
When you describe a distribution, concentrate on the main features. Look
for major peaks, not for minor ups and downs in the bars of the histogram.
Look for clear outliers, not just for the smallest and largest observations. Look
for rough symmetry or clear skewness.
SYMMETRIC AND SKEWED DISTRIBUTIONS
A distribution is symmetric if the right and left sides of the histogram are
approximately mirror images of each other.
A distribution is skewed to the right if the right side of the histogram
(containing the half of the observations with larger values) extends
much farther out than the left side. It is skewed to the left if the left side
of the histogram extends much farther out than the right side.
Here are more examples of describing the overall pattern of a histogram.
EXAMPLE 1.5 Iowa Test scores
Figure 1.4 displays the scores of all 947 seventh-grade students in the public schools
of Gary, Indiana, on the vocabulary part of the Iowa Test of Basic Skills. The
2 10 12
0
2
4
6
8
10
12
Grade-equivalent vocabulary score
Percent
of
seventh-grade
students
8
6
4
Figure 1.4 Histogram of the Iowa Test vocabulary scores of all seventh-grade
students in Gary, Indiana. This distribution is single-peaked and symmetric.

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distribution is single-peaked and symmetric. In mathematics, the two sides of symmet-
ric patterns are exact mirror images. Real data are almost never exactly symmetric.
We are content to describe Figure 1.4 as symmetric. The center (half above, half
below) is close to 7. This is seventh-grade reading level. The scores range from 2.0
(second-grade level) to 12.1 (twelfth-grade level).
Notice that the vertical scale in Figure 1.4 is not the count of students but the per-
cent of Gary students in each histogram class. A histogram of percents rather than
counts is convenient when we want to compare several distributions. To compare
Gary with Los Angeles, a much bigger city, we would use percents so that both his-
tograms have the same vertical scale.
EXAMPLE 1.6 College costs
Jeanna plans to attend college in her home state of Massachusetts. In the College
Board’s Annual Survey of Colleges, she finds data on estimated college costs for the
2002–2003 academic year. Figure 1.5 displays the costs for all 56 four-year colleges in
Massachusetts (omitting art schools and other special colleges). As is often the case,
we can’t call this irregular distribution either symmetric or skewed. The big feature of
the overall pattern is two separate clusters of colleges, 11 costing less than $16,000
clusters
and the remaining 45 costing more than $20,000. Clusters suggest that two types of
individuals are mixed in the data set. In fact, the histogram distinguishes the 11 state
colleges in Massachusetts from the 45 private colleges, which charge much more.
8 12 16 20 24 28 32 36
Annual cost of college ($1000)
0
2
4
6
8
10
Number
of
Massachusetts
colleges
Figure 1.5 Histogram of the estimated costs (in thousands of dollars) for four-year
colleges in Massachusetts. The two clusters distinguish public from private
institutions.

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15
Quantitative variables: stemplots
The overall shape of a distribution is important information about a vari-
able. Some types of data regularly produce distributions that are symmetric or
skewed. For example, the sizes of living things of the same species (like lengths
of crickets) tend to be symmetric. Data on incomes (whether of individuals,
companies, or nations) are usually strongly skewed to the right. There are many
moderate incomes, some large incomes, and a few very large incomes. Many dis-
tributions have irregular shapes that are neither symmetric nor skewed. Some
data show other patterns, such as the clusters in Figure 1.5. Use your eyes and
describe what you see.
1.6 Sports car fuel economy. Table 1.2 (page 12) gives data on the fuel
economy of 2002 model sports cars. Your histogram (Exercise 1.5) shows
an extreme high outlier. This is the Honda Insight, a hybrid gas-electric
car that is quite different from the others listed. Make a new histogram
of highway mileage, leaving out the Insight. Classes that are about
2 miles per gallon wide work well.
(a) Describe the main features (shape, center, spread, outliers) of the
distribution of highway mileage.
(b) The government imposes a “gas guzzler”tax on cars with low gas
mileage. Which of these cars do you think may be subject to the gas
guzzler tax?
1.7 College costs. Describe the center (midpoint) and spread (smallest to
largest) of the distribution of Massachusetts college costs in Figure 1.5.
An overall description works poorly because of the clusters. A better
description gives the center and spread of each cluster (public and
private colleges) separately. Do this.
Histograms are not the only graphical display of distributions. For small data
sets, a stemplot is quicker to make and presents more detailed information.
STEMPLOT
To make a stemplot:
1. Separate each observation into a stem, consisting of all but the final
(rightmost) digit, and a leaf, the final digit. Stems may have as many
digits as needed, but each leaf contains only a single digit.
2. Write the stems in a vertical column with the smallest at the top, and
draw a vertical line at the right of this column.
3. Write each leaf in the row to the right of its stem, in increasing order
out from the stem.

P1: FBQ
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
21
22
23
24
25
779
2345579
00144889
2356
13778
235
48
0229
07
04
7
3
1
8
1
7
3
These entries are 6.4%
and 6.8%
Figure 1.6 Stemplot of the
percents of Hispanic
residents in the states. Each
stem is a percent and leaves
are tenths of a percent.
EXAMPLE 1.7 Making a stemplot
For the percents of Hispanic residents in Table 1.1, take the whole-number part of
the percent as the stem and the final digit (tenths) as the leaf. The Massachusetts
entry, 6.8%, has stem 6 and leaf 8. Wyoming, at 6.4%, places leaf 4 on the same stem.
These are the only observations on this stem. We then arrange the leaves in order, as
48, so that 6 | 48 is one row in the stemplot. Figure 1.6 is the complete stemplot for
the data in Table 1.1. To save space, we left out California, Texas, and New Mexico,
which have stems 32 and 42.
The vital few?
Skewed distributions can show
us where to concentrate our
efforts. Ten percent of the cars
on the road account for half of
all carbon dioxide emissions. A
histogram of CO2 emissions
would show many cars with
small or moderate values and a
few with very high values.
Cleaning up or replacing these
cars would reduce pollution at
a cost much lower than that of
programs aimed at all cars.
Statisticians who work at
improving quality in industry
make a principle of this:
distinguish “the vital few”from
“the trivial many.”
A stemplot looks like a histogram turned on end. Compare the stemplot
in Figure 1.6 with the histogram of the same data in Figure 1.3. Both show a
single-peaked distribution that is strongly right-skewed and has some observa-
tions that we would probably call high outliers (three of these are left out of
Figure 1.6). You can choose the classes in a histogram. The classes (the stems)
of a stemplot are given to you. Figure 1.6 has more stems than there are classes
in Figure 1.3. So histograms are more flexible. But the stemplot, unlike the his-
togram, preserves the actual value of each observation. Stemplots work well for
small sets of data. Use a histogram to display larger data sets, like the 947 Iowa
Test scores in Figure 1.4.
EXAMPLE 1.8 Pulling wood apart
Student engineers learn that although handbooks give the strength of a material as
a single number, in fact the strength varies from piece to piece. A vital lesson in all
fields of study is that “variation is everywhere.”Here are data from a typical student

P1: FBQ
17
23
24
25
26
27
28
29
30
31
32
33
0
0
5
7
259
399
033677
0236
Figure 1.7 Stemplot of
breaking strength of pieces of
wood, rounded to the nearest
hundred pounds. Stems are
thousands of pounds and
leaves are hundreds of
pounds.
laboratory exercise: the load in pounds needed to pull apart pieces of Douglas fir
4 inches long and 1.5 inches square.
33,190 31,860 32,590 26,520 33,280
32,320 33,020 32,030 30,460 32,700
23,040 30,930 32,720 33,650 32,340
24,050 30,170 31,300 28,730 31,920
We want to make a stemplot to display the distribution of breaking strength. To
avoid many stems with only one leaf each, first round the data to the nearest hundred rounding
pounds. The rounded data are
332 319 326 265 333 323 330 320 305 327
230 309 327 336 323 240 302 313 287 319
Now it is easy to make a stemplot with the first two digits (thousands of pounds) as
stems and the third digit (hundreds of pounds) as leaves. Figure 1.7 is the stemplot.
The distribution is skewed to the left, with midpoint around 320 (32,000 pounds)
and spread from 230 to 336.
You can also split stems to double the number of stems when all the leaves splitting stems
would otherwise fall on just a few stems. Each stem then appears twice. Leaves
0 to 4 go on the upper stem, and leaves 5 to 9 go on the lower stem. If you
split the stems in the stemplot of Figure 1.7, for example, the 32 and 33 stems
become
32 033
32 677
33 023
33 6
Rounding and splitting stems are matters for judgment, like choosing the classes
in a histogram. The wood strength data require rounding but don’t require split-
ting stems.
1.8 Students’ attitudes. The Survey of Study Habits and Attitudes (SSHA)
is a psychological test that evaluates college students’ motivation, study
habits, and attitudes toward school. A private college gives the SSHA

P1: FBQ
to 18 of its incoming first-year women students. Their scores are
154 109 137 115 152 140 154 178 101
103 126 126 137 165 165 129 200 148
Make a stemplot of these data. The overall shape of the distribution is
irregular, as often happens when only a few observations are available.
Are there any outliers? About where is the center of the distribution
(the score with half the scores above it and half below)? What is the
spread of the scores (ignoring any outliers)?
1.9 Alternative stemplots. Return to the Hispanics data in Table 1.1 and
Figure 1.6. Round each state’s percent Hispanic to the nearest whole
percent. Make a stemplot using tens of percents as stems and percents as
leaves. All of the leaves fall on just five stems, 0, 1, 2, 3, and 4. Make
another stemplot using split stems to increase the number of classes.
With Figure 1.6, you now have three stemplots of the Hispanics data.
Which do you prefer? Why?
Time plots
Many variables are measured at intervals over time. We might, for example,
measure the height of a growing child or the price of a stock at the end of each
month. In these examples, our main interest is change over time. To display
change over time, make a time plot.
TIME PLOT
A time plot of a variable plots each observation against the time at
which it was measured. Always put time on the horizontal scale of your
plot and the variable you are measuring on the vertical scale. Connecting
the data points by lines helps emphasize any change over time.
EXAMPLE 1.9 More on the cost of college
How have college tuition and fees changed over time? Table 1.3 gives the average
tuition and fees paid by college students at four-year colleges, both public and pri-
vate, from the 1971–1972 academic year to the 2001–2002 academic year. To com-
pare dollar amounts across time, we must adjust for the changing buying power of
the dollar. Table 1.3 gives tuition in real dollars, dollars that have constant buying
power.7
Average tuition in real dollars goes up only when the actual tuition rises
by more than the overall cost of living. Figure 1.8 is a time plot of both public and
private tuition.

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The splendid promenades, the handsome buildings, and the spacious
theatres combine to make Madrid one of the first cities of the world, and the
author has endeavoured with the aid of the camera, to place every feature
and aspect of the Spanish metropolis before the reader. Some of the
illustrations reproduced here have been made familiar to the English public
by reason of the interesting and stirring events connected with the Spanish
Royal Marriage, but the greater number were either taken by the author, or
are the work of photographers specially employed to obtain new views for
the purpose of this volume.
UNIFORM WITH THIS VOLUME
GOYA
A BIOGRAPHY AND APPRECIATION. ILLUSTRATED BY
REPRODUCTIONS OF 600 OF HIS PICTURES
The last of the old masters and the first of the moderns, as he has been
called, Francisco José de Goya y Lucientes is not so familiarised to English
readers as his genius deserves. He was born at a time when the tradition of
Velazquez was fading, and the condition of Spanish painting was debased
almost beyond hope of salvation; he broke through the academic tradition
of imitation; “he, next to Velazquez, is to be accounted as the man whom
the Impressionists of our time have to thank for their most definite stimulus,
their most immediate inspiration.”
The genius of Goya was a robust, imperious, and fulminating genius; his
iron temperament was passionate, dramatic, and revolutionary; he painted a
picture as he would have fought a battle. He was an athletic, warlike, and
indefatigable painter; a naturalist like Velazquez; fantastic like Hogarth;
eccentric like Rembrandt; the last flame-coloured flash of Spanish genius.
It is impossible to reproduce his colouring; but in the reproductions of
his works the author has endeavoured to convey to the reader some idea of
Goya’s boldness of style, his mastery of frightful shadows and mysterious
lights, and his genius for expressing all terrible emotions.

UNIFORM WITH THIS VOLUME
CORDOVA
A HISTORICAL AND DESCRIPTIVE ACCOUNT OF THE ANCIENT
CITY WHICH THE CARTHAGINIANS STYLED THE “GEM OF THE
SOUTH,” WITH 160 ILLUSTRATIONS
Gay-looking, vivacious in its beauty, silent, ill-provided, depopulated,
Cordova was once the pearl of the West, the city of cities, Cordova of the
thirty suburbs and three thousand mosques; to-day she is no more than an
overgrown village, but she still remains the most Oriental town in Spain.
Cordova, once the centre of European civilisation, under the Moors the
Athens of the West, the successful rival of Baghdad and Damascus, the seat
of learning and the repository of the arts, has shrunk to the proportions of a
third-rate provincial town; but the artist, the antiquary and the lover of the
beautiful, will still find in its streets and squares and patios a mysterious
spell that cannot be resisted.
BY ALBERT F. CALVERT
LIFE OF CERVANTES
A NEW LIFE OF THE GREAT SPANISH AUTHOR TO
COMMEMORATE THE TERCENTENARY OF THE PUBLICATION OF
“DON QUIXOTE,” WITH NUMEROUS PORTRAITS AND
REPRODUCTIONS FROM EARLY EDITIONS OF “DON QUIXOTE”
Size Crown 8 vo. 150 pp. Price 3/6 net
PRESS NOTICES
“A popular and accessible account of the career of Cervantes.”—Daily
Chronicle.
“A very readable and pleasant account of one of the great writers of all
time.”—Morning Leader.

“Mr. Calvert is entitled to the gratitude of book-lovers for his
industrious devotion at one of our greatest literary shrines.”—Birmingham
Post.
“It is made trebly interesting by the very complete set of Cervantes’
portraits it contains, and by the inclusion of a valuable bibliography.”—
Black and White.
“We recommend the book to all those to whom Cervantes is more than a
mere name.”—Westminster Gazette.
“A most interesting résumé of all facts up to the present time known.”—
El Nervion de Bilbao, Spain.
“The most notable work dedicated to the immortal author of Don
Quixote that has been published in England.”—El Graduador, Spain.
“Although the book is written in English no Spaniard could have written
it with more conscientiousness and enthusiasm.”—El Defensor de
Granada, Spain.
THE ALHAMBRA
OF GRANADA, BEING A BRIEF HISTORY OF THE MOSLEM
RULE IN SPAIN FROM THE REIGN OF MOHAMMED THE FIRST TO
THE FINAL EXPULSION OF THE MOORS, TOGETHER WITH A
PARTICULAR ACCOUNT OF THE CONSTRUCTION, THE
ARCHITECTURE AND THE DECORATION OF THE MOORISH
PALACE, WITH 80 COLOURED PLATES AND NEARLY 300 BLACK
AND WHITE ILLUSTRATIONS (NEW EDITION). DEDICATED BY
PERMISSION TO H.M. KING ALFONSO XIII.
Size 10 x 7½. Price £2 2s. net
PRESS NOTICES
“It is hardly too much to say that this is one of the most magnificent
books ever issued from the English Press.”—Building World.

“One is really puzzled where to begin and when to stop in praising the
illustrations.”—Bookseller.
“The most complete record of this wonder of architecture which has ever
been contemplated, much less attempted.”—British Architect.
“A treasure to the student of decorative art.”—Morning Advertiser.
“Mr. Calvert has given us a Book Beautiful.”—Western Daily Press.
“It is the last word on the subject, no praise is too high.”—Nottingham
Express.
“May be counted among the more important art books which have been
published during recent years.”—The Globe.
“Has a pride of place that is all its own among the books of the
month.”—Review of Reviews.
“Has in many respects surpassed any books on the Alhambra which up
to the present have appeared in our own country or abroad.”—El
Graduador, Spain.
“It is one of the most beautiful books of modern times.”—Ely Gazette.
“One of the most artistic productions of the year.”—Publishers’Circular.
“The most beautiful book on the Alhambra issued in England.”—Sphere.
“The standard work on a splendid subject.”—Daily Telegraph.
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“A perfect treasure of beauty and delight.”—Keighley News.
“A magnificent work.”—Melbourne Age, Australia.
“Immense collection of fine plates.”—The Times.
“A standard work, the compilation of which would credit a life’s
labour.”—Hull Daily Mail.
MOORISH REMAINS IN SPAIN
BEING A BRIEF RECORD OF THE ARABIAN CONQUEST AND
OCCUPATION OF THE PENINSULA, WITH A PARTICULAR

ACCOUNT OF THE MOHAMMEDAN ARCHITECTURE AND
DECORATION IN THE CITIES OF CORDOVA, SEVILLE AND
TOLEDO, WITH MANY COLOURED PLATES, AND OVER 400
BLACK AND WHITE ILLUSTRATIONS, DIAGRAMS, ETC.,
DEDICATED BY PERMISSION TO H.M. KING ALFONSO XIII.
Crown 4to. (7½ × 10 ins.) Price £2 2s. net
PRESS NOTICES
“The making of this book must surely have been a veritable labour of
love; and love’s labour has certainly not been lost.”—Pall Mall Gazette.
“The best age of Moorish architecture in Spain is shown with remarkable
vividness and vitality.”—The Scotsman.
“A most gorgeous book.... We cheerfully admit Mr. Calvert into the
ranks of those whom posterity will applaud for delightful yet unprofitable
work.”—Outlook.
“A large and sumptuous volume.”—Tribune.
“The illustrations are simply marvels of reproduction.”—Dundee
Advertiser.
“One of the books to which a simple literary review cannot pretend to do
justice.”—Spectator.
“A special feature of a work of peculiar interest and value are the
illustrations.”—Newcastle Chronicle.
“The illustrations are given with a minuteness and faithfulness of detail,
and colour, which will be particularly appreciated and acknowledged by
those who are most acquainted with the subject themselves.”—Liverpool
Post.
“It is impossible to praise too highly the care with which the illustrations
have been prepared.”—Birmingham Daily Post.
“It is illustrated with so lavish a richness of colour that to turn its pages
gives one at first almost the same impression of splendour as one receives
in wandering from hall to hall of the Alcazar of Seville; and this is probably
the highest compliment we could pay to the book or its author.”—Academy.
“It is certainly one of the most interesting books of the year.”—Crown.
“The occasional delicacy of design and harmony of colour can scarcely
be surpassed ... a valuable and profusely illustrated volume.”—Guardian.

“An excellent piece of work.”—The Times.
“Mr. Calvert has performed a useful work.”—Daily Telegraph.
“A truly sumptuous volume.”—The Speaker.
“Mr. Calvert has given a very complete account of the evolution of
Moresco art.”—The Connoisseur.
FOOTNOTES:
[A] This spelling of his name resembles most that used by himself.
[B] The exact contents are as follows:
“Al Card. Farnese—Viterbo.
“A’ di 16 di Nouembre, 1570.
“E’ capitato in Roma un giouane Candiotto discepolo di Titiano, che á mio
giuditio parmi raro nella pittura; e fra l’altre cose egli ha fatto un ritratto da se stesso,
che fa stupire tutti questi Pittori di Roma. Io vorrei tratenerlo sotto l’ombra de V.S.
Illma. et Revma. senza spesa altra del vivere, ma solo de una stanza nell Palazzo
Farnese per qualche poco di tempo, cioé per fin che egli si venghi ad accomodare
meglio. Pero La prego et supplico sia contenta di scrivere al Conte Lodovico suo
Maiordomo, che lo provegghi nel detto Palazzo di qualche stanza ad alto; che V.S.
Illma. fará un’ opera virtuosa degna di Lei, e io gliene terro obligo. Et le bascio con
reverenza le mani.
“Di V.S. Illma. et Revma. humilissimo servitore.
“Julio Clovio.”
[C] The record of his burial, discovered by Señor de Beruete in the register of the
parish church of Santo Tomé, is brief: “Libro de entierros de Santo Tomé de 1601-
1614, en siete del Abril del 1614 falescio Domeniko Greco. No hizo testamento,
recibo los sacramentos, en teroso en Santo Domingo el Antigua.”
[D] Two judges were appointed to settle the dispute, which arose from the
introduction of the three Marys into the picture. The Chapter objected to their
presence. El Greco’s defence was characteristic enough—What did it matter? and,
besides, the women were a long way off. The judges disagreed; whereupon the
dispute was settled by Alezo de Montoyo as follows:
“Having seen the said painting which has been executed by the said Domeniko,
and the appraisements of the judge appointed by both parties, and other persons who
understand the said painting, its execution and admirable finish; and the reasons
which the said judges have given; and seeing that the said painting is one of the best
that I have seen; and that, if it were to be estimated for all its valuable qualities, it
would be valued at a much higher sum, which but few would care to pay for it; but, in

view of the nature of the times and the price paid generally for the paintings of great
artists in Castile; and in view of, and taking into consideration all the above and all
other points that were necessary, I find that I must order, and I do order, that for the
said painting the said Garcia de Loaysa, in the name of the said Holy Church, shall
give and pay to the said Domeniko Theotokopuli three thousand and five hundred
reals: and above this sum the said Domeniko Theotokopuli cannot ask, nor must he
ask, for anything more for the said painting; and as regards the judges for the said
workers, they say that it is improper for the Marys to be introduced into the story; as
regards this I am sending the declaration of it to some theologians versed in such
matters, that they may decide upon it.”
[E] This is another rendering of the same picture; and still another is in the
collection of Señor de Beruete, Madrid.
[F] This picture passed into the collection of the Infanta Doña Isabel Farnese, and
is now in the Museo del Prado. The ‘Assumption’ in the Church of Santo Domingo el
Antigua is a poor copy of the original picture.
[G] The picture was painted for the altar of St. Maurice, but it was rejected by
Philip II., and the commission given to a third-rate Italian. To-day the picture hangs in
the Sala Capitulare.
[H] This likeness is more striking even in another ‘Coronation of the Virgin,’ by El
Greco, in the collection of Colonel P. Bosch, Madrid.
[I] Some authorities name these saints Sta. Inez and Sta. Feda.

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