Chapter 1 Solutions
1.1. Most students will prefer to work in seconds, to avoid having to work with decimals or
fractions.
1.2. Who? The individuals in the data set are students in a statistics class. What? There are
eight variables: ID (a label, with no units); Exam1, Exam2, Homework, Final, and Project
(in units in “points,” scaled from 0 to 100); TotalPoints (in points, computed from the other
scores, on a scale of 0 to 900); and Grade (A, B, C, D, and E). Why? The primary purpose
of the data is to assign grades to the students in this class, and (presumably) the variables
are appropriate for this purpose. (The data might also be useful for other purposes.)
1.3. Exam1 = 79, Exam2 = 88, Final = 88.
1.4. For this student, TotalPoints = 2 · 86 + 2 · 82 + 3 · 77 + 2 · 90 + 80 = 827, so the grade is B.
1.5. The cases are apartments. There are five variables: rent (quantitative), cable (categorical),
pets (categorical), bedrooms (quantitative), distance to campus (quantitative).
1.6. (a) To find injuries per worker, divide the rates in Example 1.6 by 100,000 (or, redo the
computations without multiplying by 100,000). For wage and salary workers, there are
0.000034 fatal injuries per worker. For self-employed workers, there are 0.000099 fatal
injuries per worker. (b) These rates are 1/10 the size of those in Example 1.6, or 10,000
times larger than those in part (a): 0.34 fatal injuries per 10,000 wage/salary workers, and
0.99 fatal injuries per 10,000 self-employed workers. (c) The rates in Example 1.6 would
probably be more easily understood by most people, because numbers like 3.4 and 9.9 feel
more “familiar.” (It might be even better to give rates per million worker: 34 and 99.)
1.7. Shown are two possible stemplots; the first uses split 5 58 5 58
stems (described on page 11 of the text). The scores are 6 0 6 058
6 58 7 00235558
slightly left-skewed; most range from 70 to the low 90s. 7 0023 8 000035557
7 5558 9 00022338
8 00003
8 5557
9 0002233
9 8
1.8. Preferences will vary. However, the stemplot in Figure 1.8 shows a bit more detail, which
is useful for comparing the two distributions.
1.9. (a) The stemplot of the altered data is shown on the right. (b) Blank stems 1 6
should always be retained (except at the beginning or end of the stemplot), 2
2 5568
because the gap in the distribution is an important piece of information about 3 34
the data. 3 55678
4 012233
4 8
5 1
53
,54 Chapter 1 Looking at Data—Distributions
1.10. Student preferences will vary. The stemplot 9
has the advantage of showing each individual 8
score. Note that this histogram has the same 7
Frequency
shape as the second histogram in Exercise 1.7. 6
5
4
3
2
1
0
50 60 70 80 90 100
First exam scores
1.11. Student preferences may vary, but the 18
larger classes in this histogram hide a lot of 16
detail. 14
Frequency
12
10
8
6
4
2
0
40 60 80 100
First exam scores
1.12. This histogram shows more details about 7
the distribution (perhaps more detail than 6
is useful). Note that this histogram has the
5
Frequency
same shape as the first histogram in the solu-
4
tion to Exercise 1.7.
3
2
1
0
55 60 65 70 75 80 85 90 95 100
First exam scores
1.13. Using either a stemplot or histogram, we see that the distribution is left-skewed, centered
near 80, and spread from 55 to 98. (Of course, a histogram would not show the exact values
of the maximum and minimum.)
1.14. (a) The cases are the individual employees. (b) The first four (employee identification
number, last name, first name, and middle initial) are labels. Department and education level
are categorical variables; number of years with the company, salary, and age are quantitative
variables. (c) Column headings in student spreadsheets will vary, as will sample cases.
1.15. A Web search for “city rankings” or “best cities” will yield lots of ideas, such as crime
rates, income, cost of living, entertainment and cultural activities, taxes, climate, and school
system quality. (Students should be encouraged to think carefully about how some of these
might be quantitatively measured.)
,Solutions 55
1.16. Recall that categorical variables place individuals into groups or categories, while
quantitative variables “take numerical values for which arithmetic operations. . . make sense.”
Variables (a), (d), and (e)—age, amount spent on food, and height—are quantitative. The
answers to the other three questions—about dancing, musical instruments, and broccoli—are
categorical variables.
1.18. Student answers will vary. A Web search for “college ranking methodology” gives
some ideas; in recent year, U.S. News and World Report used “16 measures of academic
excellence,” including academic reputation (measured by surveying college and university
administrators), retention rate, graduation rate, class sizes, faculty salaries, student-faculty
ratio, percentage of faculty with highest degree in their fields, quality of entering students
(ACT/SAT scores, high school class rank, enrollment-to-admission ratio), financial resources,
and the percentage of alumni who give to the school.
1.19. For example, blue is by far the most popu- 40
lar choice; 70% of respondents chose 3 of the 35
10 options (blue, green, and purple). 30
Percent
25
20
15
10
5
0
orange
blue
green
red
purple
yellow
gray
black
white
brown
Favorite color
1.20. For example, opinions about least-favorite 30
color are somewhat more varied than favorite
25
colors. Interestingly, purple is liked and dis-
liked by about the same fractions of people. 20
Percent
15
10
5
0
orange
blue
green
red
purple
yellow
gray
white
black
brown
Least favorite color
1.21. (a) There were 232 total respondents. The table that follows gives the percents; for
10 .
example, = 4.31%. (b) The bar graph is on the following page. (c) For example, 87.5%
232
of the group were between 19 and 50. (d) The age-group classes do not have equal width:
The first is 18 years wide, the second is 6 years wide, the third is 11 years wide, etc.
Note: In order to produce a histogram from the given data, the bar for the first age
group would have to be three times as wide as the second bar, the third bar would have to
be wider than the second bar by a factor of 11/6, etc. Additionally, if we change a bar’s
, 56 Chapter 1 Looking at Data—Distributions
width by a factor of x, we would need to change that bar’s height by a factor of 1/x.
40
35
Age group 30
(years) Percent
Percent
25
1 to 18 4.31% 20
19 to 24 41.81% 15
25 to 35 30.17% 10
5
36 to 50 15.52%
0
51 to 69 6.03%
70 and over
19 to 24
25 to 35
36 to 50
51 to 69
1 to 18
70 and over 2.16%
Age group (years)
1.22. (a) & (b) The bar graph and pie charts are shown below. (c) A clear majority (76%)
agree or strongly agree that they browse more with the iPhone than with their previous
phone. (d) Student preferences will vary. Some might prefer the pie chart because it is more
familiar.
Strongly
50 disagree
Response percent
40
30
Mildly
20 disagree Strongly
agree
10 Mildly
agree
0
Strongly Mildly Mildly Strongly
agree agree disagree disagree
1.23. Ordering bars by decreasing height shows 25
the models most affected by iPhone sales.
Replacement percent
However, because “other phone” and ”re- 20
placed nothing” are different than the other 15
categories, it makes sense to place those two
bars last (in any order). 10
5
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1.1. Most students will prefer to work in seconds, to avoid having to work with decimals or
fractions.
1.2. Who? The individuals in the data set are students in a statistics class. What? There are
eight variables: ID (a label, with no units); Exam1, Exam2, Homework, Final, and Project
(in units in “points,” scaled from 0 to 100); TotalPoints (in points, computed from the other
scores, on a scale of 0 to 900); and Grade (A, B, C, D, and E). Why? The primary purpose
of the data is to assign grades to the students in this class, and (presumably) the variables
are appropriate for this purpose. (The data might also be useful for other purposes.)
1.3. Exam1 = 79, Exam2 = 88, Final = 88.
1.4. For this student, TotalPoints = 2 · 86 + 2 · 82 + 3 · 77 + 2 · 90 + 80 = 827, so the grade is B.
1.5. The cases are apartments. There are five variables: rent (quantitative), cable (categorical),
pets (categorical), bedrooms (quantitative), distance to campus (quantitative).
1.6. (a) To find injuries per worker, divide the rates in Example 1.6 by 100,000 (or, redo the
computations without multiplying by 100,000). For wage and salary workers, there are
0.000034 fatal injuries per worker. For self-employed workers, there are 0.000099 fatal
injuries per worker. (b) These rates are 1/10 the size of those in Example 1.6, or 10,000
times larger than those in part (a): 0.34 fatal injuries per 10,000 wage/salary workers, and
0.99 fatal injuries per 10,000 self-employed workers. (c) The rates in Example 1.6 would
probably be more easily understood by most people, because numbers like 3.4 and 9.9 feel
more “familiar.” (It might be even better to give rates per million worker: 34 and 99.)
1.7. Shown are two possible stemplots; the first uses split 5 58 5 58
stems (described on page 11 of the text). The scores are 6 0 6 058
6 58 7 00235558
slightly left-skewed; most range from 70 to the low 90s. 7 0023 8 000035557
7 5558 9 00022338
8 00003
8 5557
9 0002233
9 8
1.8. Preferences will vary. However, the stemplot in Figure 1.8 shows a bit more detail, which
is useful for comparing the two distributions.
1.9. (a) The stemplot of the altered data is shown on the right. (b) Blank stems 1 6
should always be retained (except at the beginning or end of the stemplot), 2
2 5568
because the gap in the distribution is an important piece of information about 3 34
the data. 3 55678
4 012233
4 8
5 1
53
,54 Chapter 1 Looking at Data—Distributions
1.10. Student preferences will vary. The stemplot 9
has the advantage of showing each individual 8
score. Note that this histogram has the same 7
Frequency
shape as the second histogram in Exercise 1.7. 6
5
4
3
2
1
0
50 60 70 80 90 100
First exam scores
1.11. Student preferences may vary, but the 18
larger classes in this histogram hide a lot of 16
detail. 14
Frequency
12
10
8
6
4
2
0
40 60 80 100
First exam scores
1.12. This histogram shows more details about 7
the distribution (perhaps more detail than 6
is useful). Note that this histogram has the
5
Frequency
same shape as the first histogram in the solu-
4
tion to Exercise 1.7.
3
2
1
0
55 60 65 70 75 80 85 90 95 100
First exam scores
1.13. Using either a stemplot or histogram, we see that the distribution is left-skewed, centered
near 80, and spread from 55 to 98. (Of course, a histogram would not show the exact values
of the maximum and minimum.)
1.14. (a) The cases are the individual employees. (b) The first four (employee identification
number, last name, first name, and middle initial) are labels. Department and education level
are categorical variables; number of years with the company, salary, and age are quantitative
variables. (c) Column headings in student spreadsheets will vary, as will sample cases.
1.15. A Web search for “city rankings” or “best cities” will yield lots of ideas, such as crime
rates, income, cost of living, entertainment and cultural activities, taxes, climate, and school
system quality. (Students should be encouraged to think carefully about how some of these
might be quantitatively measured.)
,Solutions 55
1.16. Recall that categorical variables place individuals into groups or categories, while
quantitative variables “take numerical values for which arithmetic operations. . . make sense.”
Variables (a), (d), and (e)—age, amount spent on food, and height—are quantitative. The
answers to the other three questions—about dancing, musical instruments, and broccoli—are
categorical variables.
1.18. Student answers will vary. A Web search for “college ranking methodology” gives
some ideas; in recent year, U.S. News and World Report used “16 measures of academic
excellence,” including academic reputation (measured by surveying college and university
administrators), retention rate, graduation rate, class sizes, faculty salaries, student-faculty
ratio, percentage of faculty with highest degree in their fields, quality of entering students
(ACT/SAT scores, high school class rank, enrollment-to-admission ratio), financial resources,
and the percentage of alumni who give to the school.
1.19. For example, blue is by far the most popu- 40
lar choice; 70% of respondents chose 3 of the 35
10 options (blue, green, and purple). 30
Percent
25
20
15
10
5
0
orange
blue
green
red
purple
yellow
gray
black
white
brown
Favorite color
1.20. For example, opinions about least-favorite 30
color are somewhat more varied than favorite
25
colors. Interestingly, purple is liked and dis-
liked by about the same fractions of people. 20
Percent
15
10
5
0
orange
blue
green
red
purple
yellow
gray
white
black
brown
Least favorite color
1.21. (a) There were 232 total respondents. The table that follows gives the percents; for
10 .
example, = 4.31%. (b) The bar graph is on the following page. (c) For example, 87.5%
232
of the group were between 19 and 50. (d) The age-group classes do not have equal width:
The first is 18 years wide, the second is 6 years wide, the third is 11 years wide, etc.
Note: In order to produce a histogram from the given data, the bar for the first age
group would have to be three times as wide as the second bar, the third bar would have to
be wider than the second bar by a factor of 11/6, etc. Additionally, if we change a bar’s
, 56 Chapter 1 Looking at Data—Distributions
width by a factor of x, we would need to change that bar’s height by a factor of 1/x.
40
35
Age group 30
(years) Percent
Percent
25
1 to 18 4.31% 20
19 to 24 41.81% 15
25 to 35 30.17% 10
5
36 to 50 15.52%
0
51 to 69 6.03%
70 and over
19 to 24
25 to 35
36 to 50
51 to 69
1 to 18
70 and over 2.16%
Age group (years)
1.22. (a) & (b) The bar graph and pie charts are shown below. (c) A clear majority (76%)
agree or strongly agree that they browse more with the iPhone than with their previous
phone. (d) Student preferences will vary. Some might prefer the pie chart because it is more
familiar.
Strongly
50 disagree
Response percent
40
30
Mildly
20 disagree Strongly
agree
10 Mildly
agree
0
Strongly Mildly Mildly Strongly
agree agree disagree disagree
1.23. Ordering bars by decreasing height shows 25
the models most affected by iPhone sales.
Replacement percent
However, because “other phone” and ”re- 20
placed nothing” are different than the other 15
categories, it makes sense to place those two
bars last (in any order). 10
5
0
e r
bil lm he
zr
ry
ian
k
g
Pa
kic
n
o Ot
Ra
er
thi
mb
sM
kB
de
No
ola
Sy
ac
Si
ow
tor
Bl
ind
Mo
W Previous phone model
