-
19
Chapter 3 Exercises 3.1 to 3.14 3.1
3.2 Frequency of using Swear Words in Conversation
3.3
It is clear in both graphs that most Americans did not move
between the years 1995 and 2000, and if they did, they stayed in
the same county. It is also easy to see that the smallest
proportion moved abroad. However, without the labels, it is much
easier to see on the bar chart that more households moved within
state than to a different state than by using a pie chart.
Comparisons of categories with similar relative frequencies can be
difficult to see with a pie chart.
-
20
3.4
% A
dmit
ting
to
Smok
ing
GradeYear
11th Grade9th Grade7th Grade200119992001199920011999
25
20
15
10
5
0
2223
13
17
3
6
Change in Tobacco Smoking 1999 to 2001 It appears that in all
three grades the percentage of students that admitted to smoking
tobacco was
less in the year 2001 than it was in 1999. However, the
reduction was greater in 7th graders (6% down to 3%) and in 9th
graders (17% down to 13%) than in 11th graders which was at the
highest of the three levels in 1999 at 23% and only decreased by
one percent to 22% in 2001.
3.5
-
21
3.6
DVD PlayerCell PhonePersonal
ComputerYesMaybeNoYesMaybeNoYesMaybeNo
0.5
0.4
0.3
0.2
0.1
0.0
What can you survive without?
Nearly half the people surveyed stated that they cannot imagine
living without their computer, but the same number could definitely
live without their DVD players (maybe they would play the DVDs on
their computer!). Less than 20% would not want to give up their DVD
players but about one third of the people surveyed would not want
to give up their cell phone. It appears that people are far less
willing to give up their computers and their cell phone, but of
these two, a higher proportion think they could live without a cell
phone than a computer.
3.7 a.
Percentage of Students passing the Exit Exam by district b. The
pass rate increased each year for San Luis Obispo High School and
the State of CA
from 2002 to 2004 with a sharp rise in 2004. However, in San
Luis Obispo County, there was a drop in the pass rate in 2003,
followed by a sharp increase in 2004 when a pass in the exam was
needed for graduation.
Pass
Rat
e as
%
DistrictYear
State of CaliforniaSan Luis Obispo CountySan Luis Obispo High
School200420032002200420032002200420032002
90
80
70
60
50
40
30
20
10
0
-
22
3.8 a.
How widespread is corruption in public service? Which elected
officials are MORE ethical? b. b.
c. Its very clear from both graphs that a moderate number and a
lot of people are the two biggest categories in the corruption
question, with the a small number category being the only other
large category. It is also clear that the Democrat Republican and
Neither categories are the largest in the ethical question.
However, because the answers in the corruption question are
ordered, it can be clearly seen in the segmented bar chart that the
most popular answers are in the middle range of the answers, a fact
that is not so obvious in the pie chart.
3.9 a.
A small number, 20%
A moderate number, 39%
A lot of people, 28%
Almost everyone, 10%
Not sure, 2%Hardly anyone,
1%
Democrats, 36%
Not sure, 6%
Neither, 15%
Both equally, 10%
Republicans, 33%
-
23
b. For both age groups, females are more unfit than the overall
age group, and men are less
unfit. However, this difference is much less marked in
adolescents who on the whole are much more unfit than their older
counterparts.
3.10 a.
b.
How accurate are your weather forecasts?
0%
10%
20%
30%
40%
50%
60%
Extremely Very Somewhat Not too Not at all Not sure
c. Both graphs clearly show that Very and Somewhat are the top
two categories. However,
as the answer choices have an order, it is easier to see in the
bar chart that the popular answers are in the more favorable end of
the categories.
-
24
3.11 a.
Christmas shopping from Mail Order Catalogues
0
0.1
0.2
0.3
0.4
0.5
0.6
Very likel
y Somewhatlikely
Not too likely Not at all likely
Response
Relative Frequency
Y2000 Y2002
The proportion of Christmas shoppers who are very likely or
somewhat likely to use the Internet has increased from 2000 to
2002, and the proportion who are not too likely or not at all
likely has decreased. However it should be noted that the vast
majority of Christmas shoppers (71%) are hesitant to do their
Christmas shopping on-line.
b.
Christmas online shopping
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Very likely Somewhatlikely
Not too likely Not at all likely
Response
Rel
ativ
e Fr
eque
ncy
Y2000Y2002
The proportion of people who felt strongly about mail order
catalogues (very likely or not at all likely) increased over the 2
year period while the proportion of those who werent too sure
decreased.
-
25
3.12 a. A bar chart would be a better choice. There are 8
categories which may cause some confusion in a pie chart.
b.
Reason for Leaving the University
0
2
4
6
8
10
12
Acad
emic
proble
ms
Poor
advis
ing
Need
a bre
ak
Econ
omic
reaso
ns
Fami
ly res
pons
ibiliti
es
To at
tend a
nothe
r sch
ool
Perso
nal p
roble
ms
Othe
r
Freq
uenc
y
c. 3.13 a. There are too many categories for this pie chart to
be effective.
b.
Roadside Hazard by Object Struck
05
1015202530
Tree
Emba
nkme
nt
Guard
rail
Pole
Ditch
Curb
Sign o
r Pos
t
Culve
rt
Fenc
e
Conc
rete B
ar
Bridg
e Rail
Othe
r
Perc
ent
This is much more effective than the pie chart. It is very easy
to compare the small differences between the objects as hazards on
the roads.
3.14 a. The number of people killed in highway work zones has
varied between 650 and 850 a year
in a cyclical way. There were two peaks, in 1994 and 1999 when
over 800 people were killed and two troughs, in 1992 and 1997 when
less than 700 were killed.
b. A pie chart would not have clearly shown the trend over
time.
-
26
Exercises 3.15 to 3.21 3.15 a. Number of people (12 and older)
who have smoked in the last month, by State
1 1 3 3 3 5 7 9 2 1 2 5 6 8 stem = hundreds (of thousands)
3 0 0 6 7 leaves = tens (of thousands) 4 5 5 4 7 6 5 8 8 7 3 4 8
6 9 1 8 9
10 2 4 11 2 7 7 8 12 1 2 13 4 14 3 7 9 15 16 6 17 8 18 19 20 1
21 22 23 4 24 25 26 27 5 28 6 7 29 30 31 32 33 6 34 35 36 37 38 39
40 5 41 42 43 44 3 45 46 47 48 49 50 51 52 53 54 55 1
-
27
b. The distribution is skewed to the right with most of the
states having values at the lower end of the scale. Forty out of
the 50 states have less than 1,500,000 people who have smoked in
the past month. There are some outliers at the high end of the
distribution. c. No, it does not indicate that tobacco is
necessarily a problem in these states. NY, CA, and
TX are the three most heavily populated states in the United
States and even if they have the same proportion of smokers as
others states, they will have a higher number of smokers because of
the greater population.
d. No, it would be better to use the proportion of the
population of each state that smoked
during the past month. That way, the population of the state
would not affect the result. 3.16
Calorie Content (cal/100ml)of 26 Brands of Light Beers
1 9 stem: tens 2 2 3 7 8 8 9 9 9 leaf: ones 3 0 0 1 1 1 2 2 3 3
4 5 9 4 0 1 2 3
Most brands of light beers have calorie contents of between 27
and 35 cal/100ml. 4 of the brands have a lower calorie content
(between 19 and 23 cal/100ml) and another four have a higher
calorie content (between 39 and 43 cal/100ml)
3.17
Calorie Content (cal/100ml)of 26 Brands of Light Beers
1L stem: tens 1H 9 leaf: ones 2L 2 3 2H 7 8 8 9 9 9 3L 0 0 1 1 1
2 2 3 3 4 5 3H 9 4L 0 1 2 3 4H
3.18 a.
% of fully credentialed teachers in CA counties 7 5 stem: tens 8
0 3 3 4 5 5 5 5 5 6 7 8 8 8 9 9 leaf: ones 9 0 0 1 1 1 1 2 2 3 4 4
4 4 5 5 5 5 5 5 5 5 6 6 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 9 9 10 0
Most counties in California have over 90% of their teachers
fully credentialed. Los Angeles County is the lowest with only 75%
and Alpine is the only County where 100% of their teachers are
fully credentialed.
-
28
b. % of fully credentialed teachers in CA counties 7L 7H 5 stem:
tens 8L 0 3 3 4 leaf: ones 8H 5 5 5 5 5 6 7 8 8 8 8 9 9 9L 0 0 1 1
1 1 2 2 3 4 4 4 4 9H 5 5 5 5 5 5 5 5 6 6 7 7 7 7 7 7 7 7 7 8 8 8 8
8 9 9 10L 0
We can now see that there are only three counties with less then
85% of their teachers fully credentialed.
3.19 a.
Very Large Urban Areas Large Urban Areas 2 3 6 9
8 3 0 0 3 3 5 8 9 9 9 4 0 3 6 6 stem = tens
1 1 7 8 5 0 1 2 3 5 5 leaves = units 0 3 7 9 6
2 7 8
3 9
b. Not necessarily. Philadelphia is a larger urban area than
Riverside, CA, but has less extra travel time. However, overall,
taking into account all the urban areas mentioned, or if we were to
calculate the average or typical value for each type of area, then
we would find that on the whole, the larger the urban area, the
greater the extra travel time.
3.20 a. % increase in population 1990 to 2000
0 0 1 3 4 4 4 5 5 5 5 6 7 8 8 8 8 9 9 9 9 9 1 0 0 0 0 0 0 1 1 2
3 4 4 4 4 5 7 8 stem: tens 2 0 0 1 1 3 3 6 8 leaf: ones 3 0 1 4 0 5
6 6
b. 48 of the states have an increase in population of 31% or
less, and most of these are under
12%. There are two states that have a much larger %increase:
Nevada (66%), and Arizona (40%)
c. % increase in population 1990 to 2000
WEST EAST 9 9 8 8 8 0 0 1 3 4 4 4 5 5 5 5 6 7 8 9 9 9
4 4 3 0 1 0 0 0 0 0 1 1 2 4 4 5 7 8 8 3 1 0 0 2 1 3 6
1 0 3 0 4 stem: tens
5 leaf: ones 6 6
The States that show a large % increase in population are in the
West. There are 5 states in the West (out of 19) that has a %
increase greater than the maximum increase in the East.
-
29
3.21
High School drop out rates 1997-1999 by State 0f 5 5 5 0s 6 6 6
6 6 7 7 7 7 7 7 7 stem: tens 0* 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9
leaf: ones 1. 0 0 0 1 1 1 1 1 1t 2 2 2 2 3 3 3 3 1f 1s 7 7
Exercises 3.22 to 3.34 3.22 a. Relative Frequency Distribution
for Drug Plan Costs
Class Interval Frequency Relative Frequency $0 -
-
30
3.23 a.
Balance
Den
sity
1500
070
0020
0010
005000
0.0020
0.0015
0.0010
0.0005
0.0000
Credit Card Balance (in $) Credit Card Bureau Data)
b.
Balance
Den
sity
1500
070
0030
0020
0010
00500
1000
0.0020
0.0015
0.0010
0.0005
0.0000
Credit Card Balance (in $) Survey Data
c. The results for both the survey and the credit bureau show
that most college student debt is less than $2000. However, the
results dont agree exactly; the credit card bureau had more
students with very large debt than the survey data suggested. Maybe
some of the students with very large debts were reluctant to admit
to the scale of their problems!
d. Only 132 out of 1260 students replied, an 89.5% nonresponse
rate. It may be that students
with a large debt would be reluctant to respond, so this sample
was not representative of all students.
-
31
3.24 a.
Number of Impairments
Frequency Relative Frequency
0 100 .4167 1 43 .1792 2 36 .1500 3 17 .0708 4 24 .1000 5 9
.0375 6 11 .0458 n = 240 1.0000
b. .4167 + .1792 + .1500 = .7459 c. 1 .7459 = .2541 d. .1000 +
.0375 + .0458 = .1833 3.25 a.
0 200 400 600 800
0
.10
.20
.30
.40
.50
.60
# Mins Used
Rel
ativ
e F
requ
ency
Average # Cell phone mins used per Month by Men
Most men average between 0 and 200 mins a month. Far fewer
average between 400 and 800 mins a month.
b.
0 200 400 600 800
0
.10
.20
.30
.40
.50
.60
# Mins used
Rel
ativ
e Fr
eque
ncy
Average # Cell phone mins used per Month by Women
The distribution for men and women is similar in that most women
average between 0 and
200 mins as do men. Fewer women average 600 to 800 minutes than
men.
-
32
c. .18 + .56 = .74
d. .79=.1.74+ 2
e. .13*3+.08=.17754
3.26 a. If a commute is longer than 45 minutes, then the time is
often rounded to the nearest 15 or 30
minutes. b
Commute Time Frequency Relative Frequency Density 0 to < 5
5200 .0518 .0104 5 to < 10 18200 .1813 .0363
10 to < 15 19600 .1952 .0390 15 to < 20 15400 .1534 .0390
20 to < 25 13800 .1375 .0307 25 to < 30 5700 .0568 .0275 30
to < 35 10200 .1016 .0114 35 to < 40 2000 .0199 .0203 40 to
< 45 2000 .0199 .0040 45 to < 60 4000 .0398 .0027 60 to <
90 2100 .0209 .0007 90 to < 120 2200 .0219 .0007
c.
Most working adults commute between 10 minutes and an hour to
work. However, there are a still a surprising number (look at the
area) that commute between one and two hours to work.
d. Commute Time Relative Frequency Cumulative Relative
Frequency
0 to < 5 .0518 .0518 5 to < 10 .1813 .2331
10 to < 15 .1952 .4283 15 to < 20 .1534 .5817 20 to <
25 .1375 .7192 25 to < 30 .0568 .7760 30 to < 35 .1016 .8776
35 to < 40 .0199 .8975 40 to < 45 .0199 .9174 45 to < 60
.0398 .9572 60 to < 90 .0209 .9781 90 to < 120 .0219 1.0
-
33
0 50 100
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
timecu
m f
req.
i 0.93 ii 0.34 iii 17 mins 3.27 a.
0 360, 340, 960, 530, 540, 960, 450, 500, 100, 510, 240, 396 1
280, 240, 050, 000, 320, 250, 120, 850, 670, 890, 419 2 100, 400,
120, 250, 320, 400, 460, 700, 730, 109 3 060, 330, 380, 350, 870,
150, 150 4 390, 770 5 320, 700, 220, 850, 770
stem: thousands digit leaf: hundreds, tens and ones
The stem and leaf display suggests that a typical or
representative value is in the stem 2 row, perhaps someplace in the
2230 range. The display declines as we move to higher stems and
then rises at stem 5 row. There are no gaps in the display. The
shape of the display is not perfectly symmetric but rather appears
to stretch out quite a bit in the direction of low stems.
b.
Class Interval Frequency Relative Frequency 0 -
-
34
The upper tail of the histogram stretches farther than the lower
tail so the histogram is positively skewed.
c. The proportion of subdivisions with total length less than
2000 is 47
1112 + = 4723 = .4894 or
approximately 49%.
The proportion of subdivisions between 2000 and 4000 is
3617.47
710 =+ or approximately 36%.
3.28 a. We dont know the width of the last interval 100,000 or
more and the widths of the intervals
are unequal. b.
c. Only 42.7% of medical student who have completed their
residencies have educational debts of under $5,000. 41.8% of them
have educational debts of between $50,000 and $150,000. It seems
that medical students finishing their residency have either a very
large debt or a relatively small debt with only 15.5% of them
having a debt of between $5,000 and $50,000.
3.29 a. If the exam is quite easy, then there would be a large
number of high scores with a small
number of low scores. The resulting histogram would be
negatively skewed. b. If the exam were quite hard, then there would
be a large number of low scores with a small
number of high scores. The resulting histogram would be
positively skewed. c The students with the better math skills would
score high, while those with poor math skills
would score low. This would result in basically two groups and
thus the resulting histogram would be bimodal.
3.30 a. and b.
Classes Frequency Rel. Freq. Cum. Rel. Freq. 0 < 6 2 .0225
.0225
6 < 12 10 .1124 .1349 12 < 18 21 .2360 .3709 18 < 24 28
.3146 .6855 24 < 30 22 .2472 .9327 30 < 36 6 .0674
1.00011.0
n = 50 1.0000
c. (Rel. Freq. for 12 < 18) = (Cum. Rel. Freq. for < 18)
(Cum. Rel. Freq. for < 12) = .3709 .1349 = .2360.
-
35
d. i The proportion that had pacemakers that did not malfunction
within the first year equals 1 minus the proportion that had
pacemakers that malfunctioned within the first year (12 months),
which is 1 .1349 = .8651.
ii The proportion that required replacement between one and two
years after
implantation is equal to the proportion that had to be replaced
within the first 2 years (24 months) minus the proportion that had
to be replaced within the first year (12 months). This is 0.6855
0.1349 = 0.5506.
e.
i. Approximately 20 months ii. Approximately 29 months
3.31 a.
Class Intervals
Frequency Rel. Freq. Density
.15 < .25 8 .02192 0.2192
.25 < .35 14 .03836 0.3836
.35 < .45 28 .07671 0.7671
.45 < .50 24 .06575 1.3150
.50 < .55 39 .10685 2.1370
.55 < .60 51 .13973 2.7946
.60 < .65 106 .29041 5.8082
.65 < .70 84 .23014 4.6028
.70 < .75 11 .03014 0.6028 n = 365 1.00001
-
36
b. The proportion of days with a clearness index smaller than
.35 is (8 14) 22 .06365 365+ = = , which
converts to 6%.
c. The proportion of days with a clearness index of at least .65
is (84 11) 95 .26365 365+ = = , which
converts to 26%. 3.32 Almost all the differences are positive
indicating that the runners slow down. The graph is positively
skewed. A typical difference value is about 150. About .02 of
the runners ran the late distance more quickly that the early
distance.
3.33
This histogram is symmetric.
This histogram is positively skewed.
-
37
This is a bimodal histogram. While it is not perfectly symmetric
it is close to being symmetric.
This is a bimodal histogram.
This is a negatively skewed histogram.
-
38
3.34
Class Intervals I II III IV 100 < 120 5 5 35 20 120 < 140
10 7 15 10 140 < 160 40 10 10 4 160 < 180 10 15 5 25 180 <
200 5 33 5 11
a. The histogram associated with frequency set I would be
symmetric. b. The histogram associated with frequency set IV would
be bimodal. c. The histogram associated with frequency set III
would be positively skewed. d. The histogram associated with
frequency set II would be negatively skewed. Exercises 3.35 to 3.45
3.35 a. There are several values that have identical or nearly
identical x-values yet different y-
values. Therefore, the value of y is not determined solely by x
, but also by various other factors. There appears to be a tendency
for y to decrease as x increases.
b. People with low body weight tend to be small people and it is
possible their livers may be
smaller than the liver of an average person. Conversely, people
with high weight tend to be large people and their livers may be
larger than the liver of an average person. Therefore, we would
expect the graft weight ratio to be large for low weight people and
small for high weight people.
3.36 In general, there appears to be a positive relationship
between drop-out rate and poverty
rate. On average, as the poverty rate increases, the drop-out
rate increases. 3.37 a.
There is a tendency for y to increase as x does. That is, larger
values of gross efficiency tend to be associated with larger values
of percentage type I fibers (a positive relationship between the
variables).
-
39
b. There are several observations that have identical x-values
yet different y-values (for
example, ). Thus, the value of y is not determined solely by x,
but also by various other factors.
6 7 6 750, 20.5 20.1x x but y and y= = = =
3.38 a.
b.
c. There appears to be a negative relationship between age and
emissions. As age increases,
emissions decrease. d. The two scatterplots have very similar
patterns. As engine age increases beyond age = 8
years, there is a definite decrease in emissions in both plots.
For age = 0, there are several different y-values which indicates
that emissions are not solely determined by age.
-
40
3.39 There are several observations that have identical or
nearly identical x-values yet different y-values.
Therefore, the value of y is not determined solely by x, but
also by various other factors. There appears to be a general
tendency for y to decrease in value as x increases in value. There
are two data points which are far removed from the remaining data
points. These two data points have large x-values and small
y-values. Their presence might have an undue influence on a line
fit to the data.
3.40 a. There is not a deterministic relationship between x and
y. This can be determined by the fact
that there are two data points, (100, 222) and (100, 241), which
have the same x-value but different y-values.
b.
c. There appears to be a tendency for oxygen consumption rate to
increase as plasma cortisol
concentration increases. 3.41 a.
1985 1990 1995 2000
10
20
30
40
50
Year
%
% of Households w ith a Computer
b. There has been an increase in the ownership of computers over
time since 1985. At first the
increase was slow and then from 1995 the increase has been
increasing at a more rapid rate.
-
41
3.42 a.
Year
Hom
e si
ze
2003199019701950
2400
2200
2000
1800
1600
1400
1200
1000
Is the Average Home Size Changing with Time?
b. I would be expect the average home size to be approximately
2500 ft2 by 2010. 3.43 a.
Percentage that thought it was a Good Time to buy a House
Sep 2003
Jun 2003Mar 1991
Mar 1978
0102030405060708090
1977 1982 1987 1992 1997 2002
Date
Perc
enta
ge
-
42
b. Percentage that thought it was a Good Time or a Bad Time to
buy a
House over Time
Sep 2003Jun 2003
Mar 1991Mar 1978Mar 1978 Mar 1991 Sep 2003
Jun 20030
20
40
60
80
100
1977 1982 1987 1992 1997 2002
Date
Perc
enta
ge Good TimeBad Time
c. The time series plot gives a better trend over time as it
shows a time scale, which the bar chart does not.
3.44 a.
Year
Ave
rage
Fat
alit
ies
20001995199019851980
200
180
160
140
120
100
MonTueWedThursFriSatSun
Variable
Average Traffic Fatalities per Week by Day
b. There are many more fatalities on a Friday, Saturday and
Sunday. Most people work Monday to Friday and tend to go drive more
on at the weekend. c. There has been a steady decrease in the
average number of fatalities between 1980 and
2000, more so on Fridays to Sundays than Mondays to Thursdays.
This could be because most states introduced the compulsory use of
front, and then rear seat belts in cars during this time.
3.45 In both 2001 and 2002 the box office sales dropped in Weeks
2, 6 and in the last two weeks of the summer. The seasonal peaks
occurred during Weeks 4, 9 and 13.
-
43
Exercises 3.46 to 3.84 3.46
Average Verbal SAT defined by First Language
519
486
462
430440450460470480490500510520530
English English and anotherLanguage
A language other thanEnglish
SAT
scor
e
3.47
Average Verbal and Math scores for the Language Groups
519
486
462
521513
521
430440450460470480490500510520530
English English andanother
Language
A languageother than
English
SAT
scor
es
Verbal SATMath SAT Score
For those students who have English as a first language there is
very little difference between the average Verbal and Math scores.
For students who speak English and another language, they do less
well in both subjects, but it is more noticeable in the Verbal
scores. Those students who speak a language other than English as
their first language score on average about 55 points less than
those who speak only English. However, their average Math scores
are as high as the English only speaking students.
-
44
3.48
What is most important for Children?
0
0.1
0.2
0.3
0.4
0.5
0.6
Grades Popular Sports
Rel
ativ
e Fr
eque
ncy
Boys Girls 3.49
3.50
Other Studios Disney 00012 0L 00001233
59 0H 57 1 1L
56 1H 567 0 2L 02
2H 9 3L Stem: Hundreds 3H Leaves: Tens (truncated) 4L 4H 5L
4
The first impression is that there are many films where the
tobacco exposure time is small, both for Disney films and for those
made by other studios. Disney has made more films with longer
exposure to tobacco and there is an obvious outlier in the Disney
data.
-
45
3.51 a.
Av. Transp. Exp. for a British household (in Pounds
Sterling)
b. The time-series plots form part (a) do agree with the
statement. It is clear from the first graph
that the actual expenditure has been increasing. Although the
percentage of household expenditure looks volatile, in the 10 years
of this study, it has varied from 14.9% to 17.2%, and is small
compared with the increase in actual expenditure.
Year
Av.
Tra
nsp.
Exp
endi
ture
400
375
350
325
300
275
250
20001999199819971996199519941993199219911990
Year
Perc
enta
ge
20001999199819971996199519941993199219911990
17.5
17.0
16.5
16.0
15.5
15.0
Percentage of Household expenses spent on Transportation
-
46
3.52
Gender
0
0.
0.
0.
0.
0.
0.
Advantage being a
Advantagbeing a
No Don't
Respons
Relative
WomenMe
More than half the women think that it is an advantage to be a
man and a third think theres no advantage for either gender. Very
few men (and even fewer women) think that its an advantage being a
woman.
3.53 a.
Same Salary for Same Work?
0 0.1
0.2 0.3
0.4 0.5
0.6 0.7
0.8
Man earns more
Woman earnsmore
Both earn thesame
Don't know
Relative Frequency
WomenMe
b.
-
47
c. Its much easier to compare the differences using the
comparative bar chart. The categories are next to each other and
any difference is easy to see. To compare the size of the slice
between two pie charts is more difficult.
d. The majority of both men and women think that men earn more
money for the same work.
Very few men or women think that a woman earns more. More women
than women think that a man earns more or earns the same as
woman.
3.54 a.
Home alone?
Never
Some of the Time
Most of the Time
All of the Time
b.
Home
Never
Some of the Time
Most of the Time
All of the Time
0102030405060708090
100
c. It is easier to see the difference in the proportions with a
pie chart, however it is easier to estimate the percentage of each
response with a segmented bar chart.
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48
3.55 a.
Who would you prefer to work for?
Prefer to work for a Man
Prefer to work for a Woman
No difference
No opinion
Given the choice, most people dont mind whether they work for a
man or a woman. Of those that do have an opinion, most would prefer
to have a male boss.
b.
Would would you prefer to work for?
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
No opinion
No difference
Prefer to work for aWomanPrefer to work for a Man
3.56 a. 2.2 liters/min.
b. In the row with stem of 8. The leaf of 9 would be placed to
the right of the other leaves. c. A large number of flow rates are
between 6.0 and 8.0. Perhaps 6.9 or 7.0 could be selected
as a typical flow rate.
-
49
d. There appears to be quite a bit of variability in the flow
rates. While there are a large number of flow rates in the 6.0 to
9.0 range, the flow rates appear to vary quite a bit in relation to
one another. e. The distribution is not symmetric. Taking 7.0 as a
typical value, the smaller flow rates are
spread from 2.2 to 7.0, while the larger flow rates are spread
from 7.0 to 18.9 (a larger spread).
f. The value 18.9 appears to be somewhat removed from the rest
of the data and hence is an
outlier.
Class Interval
Frequency Rel. Freq.
30 < 50 2 .04 50 < 70 4 .08 70 < 90 4 .08 90 < 110
11 .22 110 < 130 12 .24 130 < 150 3 .06 150 < 170 5 .10
170 < 190 4 .08 190 < 210 3 .06 210 < 230 1 .02 230 <
250 1 .02
n = 50 1.00 3.57
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50
3.58 How much does a Hurricane Cost?
The peaks coincide with a major hurricane (or several major
ones) hitting mainland causing loss of buildings and life. The top
5 costliest hurricanes were: Katrina (2005), Andrew (1992), Charley
(2004), Ivan (2004) and Wilma (2005).
3.59
0 6 7 5 8 9 0 0 5 0 1 8 6 1 5 2 1 6 7 0 6 3 1 2 2 8 4 3 1 8 0 8
7 8 7 7 2 5 6 9 0 7 8 6 9 0 6 1 9 7 1 3 7 5 5 0 0 0 1 5 0 5 4 5 6 7
8 2 3 0 5 6 7 1 stem: tens digit 7 0 leaf: ones digit
The data values are concentrated between 0 to 40, with a few
larger values. Overall, the plot appears to be skewed to the
right.
3.60 a.
Day of Week Frequency Sunday 109 Monday 73 Tuesday 97 Wednesday
95 Thursday 83 Friday 107 Saturday 100 n = 664
Year
Cost
60
50
40
30
20
10
020042002200019981996199419921990
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51
b. ( )107 100 109 316 .4759664 664
+ + = = , which converts to 47.59%.
c. If a murder were no more likely to be committed on some days
than on other days, the proportion of murders on a specific day
would be 1/7 = .1429. So, for three days the proportion would be
3(.1429) = .4287. Since the proportion for the weekend is .4759,
there is some evidence to suggest that a murder is more likely to
be committed on a weekend day than on a non-weekend day.
3.61 If 39% of those with critical housing needs lived in urban
areas and 42% lived in suburban areas, then 19% (100 39 42) lived
in rural areas.
Area of those with Critical Housing needs
Urban
Suburban
Rural
3.62 a.
1994 1995 1996 1997 1998 1999 2000 2001
2500
3000
3500
4000
Year
Num
ber o
f don
ors
Living-donor Transplants by Relative
The number of transplants from a living relative has been
increasing steadily from 1994 to 2001.
-
52
b.
Living-donor Kidney Transplants
0500
10001500200025003000350040004500
1994 1995 1996 1997 1998 1999 2000 2001
relatedunrelated
There are many more related donors than unrelated donors used
for kidney transplants. However the use of non-related donors is
rising at a faster rate than that of non-related donors.
3.63 a. The two histograms do give different impressions about
the distribution of values. For the
first histogram, it appears that more frozen meals have sodium
content around 800mg. However, the second histogram suggests that
sodium content is fairly uniform from 300mg to 900mg and then drops
off above 900mg.
b. Using the first histogram, the proportion of observations
that are less than 800 is
approximately
+ +
= =+ + +
106 7 182 .6667.(6 7 10 4) 27
Using the second histogram, the proportion of observations that
are less than 800 is approximately
+ + + + = = =+ + + + +
800 7506 5 5 (6)16 2 18150 .6667.
(6 5 5 6 4 1) 27 27
The actual proportion is = =18 2 .6667.27 3
3.64 a. Class Frequency Rel. Freq.
.175 < .225 4 .0727
.225 < .275 2 .0364
.275 < .325 16 .2909
.325 < .375 15 .2727
.375 < .425 9 .1636
.425 < .475 6 .1091
.475 < .525 2 .0364
.525 < .575 0 .0000
.575 < .625 1 .0182 n = 55 1.0000
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53
b. The histogram is skewed slightly in the positive direction.
The majority of the observations
are in the center.
