ALL 17 CHAPTERS COVERED
SOLUTIONS MANUAL
,Contents
1 Methods of Collecting and Presenting Data 1
2 Measures of Location and Dispersion 27
3 Probability and Common Probability Distributions 37
4 Point Estimation 51
5 Confidence Intervals and Hypothesis Tests—One Sample 59
6 Confidence Intervals and Hypothesis Tests—Two Samples 73
7 Tolerance Intervals and Prediction Intervals 83
8 Simple Linear Regression, Correlation and Calibration 87
9 Multiple Regression 101
10 Mechanistic Models 117
11 Control Charts and Quality Improvement 121
12 Design and Analysis of Experiments 139
13 Measurement System Appraisal 155
14 Reliability Analysis and Life Testing 157
15 Analysis of Categorical Data 163
16 Distribution-Free Procedures 171
17 Tying It All Together 175
, Modern Engineering Statistics: Solutions Manual to Accompany
by Thomas P. Ryan
Copyright © 2007 John Wiley & Sons, Inc.
/
Methods of Collecting and Presenting Data
Note: The data in the following exercises, including data in MIN1TABfiles(i.e.,
the files with the MTW extension), can be found at the website for the text:
ftp://ftp.wiley.com/public/sci_tech med/engineeringstatistics. This also applies to
the other chapters in the text.
1.1. Given below are the earned run averages (ERAs) for the American League for
1901-2003 (in ERAMC MTW), with the years 1916 and 1994 corrected from the
source, Total Baseball, 8th edition, by John Thorn, Phil Birnbaum, and Bill
Deane, since those two years were obviously in error. (The league started in
1901.)
Year 1901 1902 1903 1904 1905 1906 1907 1908
1909 1910 1911 1912 1913 1914
ERA 3.66 3.57 2.96 2.60 2.65 2.69 2.54 2.39
2.47 2.51 3.34 3.34 2.93 2.73
Year 1915 1916 1917 1918 1919 1920 1921 1922
1923 1924 1925 1926 1927 1928
ERA 2.93 2.82 2.66 2.77 3.22 3.79 4.28 4.03
3.98 4.23 4.39 4.02 4.14 4.04
Year 1929 1930 1931 1932 1933 1934 1935 1936
1937 1938 1939 1940 1941 1942
ERA 4.24 4.64 4.38 4.48 4.28 4.50 4.45 5.04
4.62 4.79 4.62 4.38 4.15 3.66
Year 1943 1944 1945 1946 1947 1948 1949 1950
1951 1952 1953 1954 1955 1956
ERA 3.29 3.43 3.36 3.50 3.71 4.29 4.20 4.58
4.12 3.67 3.99 3.72 3.96 4.16
Year 1957 1958 1959 1960 1961 1962 1963 1964
1965 1966 1967 1968 1969 1970
ERA 3.79 3.77 3.86 3.87 4.02 3.97 3.63 3.62
3.46 3.43 3.23 2.98 3.62 3.71
Year 1971 1972 1973 1974 1975 1976 1977 1978
1979 1980 1981 1982 1983 1984
ERA 3.46 3.06 3.82 3.62 3.78 3.52 4.06 3.76
4.21 4.03 3.66 4.07 4.06 3.99
Year 1985 1986 1987 1988 1989 1990 1991 1992
1993 1994 1995 1996 1997 1998
ERA 4.15 4.17 4.46 3.96 3.88 3.90 4.09 3.94
4.32 4.80 4.71 5.00 4.57 4.65
Year 1999 2000 2001 2002 2003
ERA 4.86 4.91 4.47 4.46 4.52
/
, 2 METHODS OF COLLECTING AND PRESENTING DA TA
Construct a time sequence plot, either by hand or using software such as
MTNITAB, or equivalently a scatterplot with ERA plotted against Year. Does the
plot reveal a random pattern about the overall average for these 103 years, or does
the plot indicate nonrandomness and/or a change in the average?
Solution:
Here is the time sequence plot that is actually in the form of a scatterplot.
(a) There is considerable nonrandomness in this plot, especially the strong
upward trend since about 1970 as well as the monotonicity during certain intervals
of years (e.g., strictly decreasing from 1938-43.)
1.3. Construct a dotplot for the data in Example 12
Solution:
, METHODS OF COLLECTING AND PRESENTING DA TA 3
1.5. Statistical literacy is important not only in engineering but also simply as a
means of expression. There are many statistical guffaws that appear in lay
publications. Some of these are given in the "Forsooth" section of RSS News
(Royal Statistical Society News) each month. Others can be found online at
Chance Nws, whose website is at the following URL:
http://www.dartmouth.edu/~chance/chance_news/news.html. The following two
statements can be found at the latter website. Explain what is wrong with each
statement.
(a) Migraines affect approximately 14% of women and 7% of men, that's one-
fifth the population (Herbal Health Newsletter Issue I)
(b) Researchers at Cambridge University have found that supplementing with
vitamin C may help reduce the risk of death by as much as 50% (Higher Nature
Health News No. HN601, 2001).
(Comment: Although the errors in these two statements should be obvious,
misstatements involving statistical techniques are often made, even in statistics
books, that are not obvious unless one has a solid grasp of statistics )
Solution:
(a) The percentages are not additive since neither is based on 100% of the
population of men and women combined. More specifically, even if the number of
women was the same as the number of men, the base would be doubled if the
populations were combined, rather than staying at the common number, as would
be necessary for the percentages to be additive.
,4 METHODS OF COLLECTING AND PRESENTING DA TA
(b) The risk will always be 100% ... regardless of the amount of Vitamin C that
is ingested!
1.7. Consider Figure 1.5. The data are as follows (in 75-25PERCENTILES2002.MTW):
SAT 75th a c c e p t a n c e SAT 25th
Row percentile rate percentile
1 1540 12 1350
2 1580 11 1410
3 1550 16 1380
4 1580 13 1450
5 1560 16 1410
6 1560 13 1360
7 1490 23 1310
8 1500 26 1300
9 1510 13 1310
10 1520 21 1330
11 1490 44 1280
12 1470 33 1290
13 1510 23 1310
14 1450 30 1290
15 1490 16 1290
16 1480 32 1300
17 1460 45 1300
18 1460 31 1270
19 1430 34 1270
20 1450 26 1200
21 1410 39 1200
22 1400 55 1220
23 1460 36 1280
24 1400 29 1170
25 1380 49 1220
26 1410 26 1240
27 1340 37 1130
28 1410 41 1230
29 1370 38 1160
30 1450 22 1280
31 1420 29 1250
32 1420 48 1220
33 1400 34 1210
34 1410 50 1240
35 1390 32 1220
36 1450 71 1240
37 1365 46 1183
38 1420 57 1250
39 1290 63 1060
40 1275 57 1070
41 1330 79 1130
42 1270 78 1050
43 1290 48 1080
44 1350 36 1150
45 1370 73 1180
46 1290 66 1070
47 1290 47 1090
48 1310 62 1090
49 1390 73 1210
, METHODS OF COLLECTING AND PRESENTING DA TA S
(a) Construct the graph of the acceptance rate against the 75th percentile SAT
score with the latter on the horizontal axis. Is the slope exactly the same as the
slope of Figure 1.5? Explain why the slope should or should not be the same.
(b) Construct the graph of the 25th percentile SAT score against the acceptance
rate with the former on the vertical axis. (The data on the 25th percentile are in
the third column in the file.) Does the point that corresponds to point #22 in
Figure 1.5 also stand out in this graph?
(c) Compute the difference between the 75th percentile and 25th percentile for
each school and plot those differences against the acceptance rate. Note that
there are two extreme points on the plot, with differences of 250 and 130,
respectively One of these schools is for a prominent public university and the
other is a private university, both in the same state. Which would you guess to be
the public university?
Solution:
(a) No, the slopes (of a line fit through the points, for example) will not be the
same because the axes are reversed.
(b) No, there are no points on the graph that stand out as being unusual.
(c) We would guess that the point with the higher acceptance rate would be the
public university (which it is: University of California —Berkeley)
1.9. Consider different amounts of one-dimensional data. What graphical display
would you recommend for each of the following numbers of observations: (a) 10,
(b) 100, and (c) 1000?
Solution:
(a) dotplot (b) dotplot or histogram (c) histogram
1.11. The following numbers are the first 50 of 102 chemical data measurements
of color from a leading chemical company that were given in Ryan (2000): 0.67,
0.63, 0.76, 0.66, 0.69, 0.71, 0.72, 0.71, 0.72, 0.72, 0.83, 0.87, 0.76, 0.79, 0.74,
0.81, 0.76, 0.77, 0.68, 0.68, 0.74, 0.68, 0.68, 0.74, 0.68, 0.69, 0.75, 0.80, 0.81,
0.86, 0.86, 0.79, 0.78, 0.77, 0.77, 0.80, 0.76, 0.67, 0.73, 0.69, 0.73, 0.73, 0.74,
0.71, 0.65, 0.67, 0.68, 0.71, 0.69, and 0.73.
(a) What graphical display would you suggest if it was suspected that there may
be some relationship between consecutive measurements (which would violate one
of the assumptions of the statistical methods presented in later chapters)?
(b) Construct the display that you suggested in part (a). Do consecutive
observations appear to be related?
, 6 METHODS OF COLLECTING AND PRESENTING DA TA
Solution:
(a) Time sequence plot or autocorrelation plot, preferably the latter.
(b) The autocorrelation function plot (the correlation between units one unit
apart, two units apart...) is given below. There does appear to be autocorrelation,
especially of observations one or two units apart since the autocorrelations for the
first two lags are above the upper decision line (95% confidence interval) and the
/-statistics exceed 2, as can be seenfromthe numbers below the graph.)
Autocorrelation Function for C1
10
c ~
o _
06 _
(0 0<
02 -
<D
00
-
t
o
o
-0?
_
o ■ 04
~
■ •=!
-08 ~
< -10 ~
~ "i ~\—■ r
2 7 12
Lag Con T LBQ Lag Corr T LBQ
1 058 411 1795 8 -034 -155 4389
2 042 230 27 56 9 -0.36 -157 5201
3 0.31 153 32 79 10 -0 46 -194 65 86
4 017 081 3443 11 -0.37 -1.46 75.10
5 0 06 0 30 3466 12 -0 23 -0 86 7866
6 -0 02 -011 3469
7 -019 -0 89 36 88
1.13. This exercise illustrates how the choice of the number of intervals greatly
influences the shape of a histogram. Construct a histogram of the first 100
positive integers for the following numbers of classes: 3, 4, 6, 7, 10, and 12. (The
number of classes can be specified in MINITAB, for example, by using the NINT
subcommand with the HIST command, and the sequence MTB>SET Cl,
DATA>1:100, DATA>END will place the first 100 integers in the first column of
the worksheet.) We know that the distribution of numbers is uniform over the
integers 1-100 because we have one of each. We also have the same number of
observations in the intervals 1-9, 10-19, 20-29, and so on. Therefore, the
histograms should theoretically be perfectly flat Are any of the histograms flat?
In particular, what is the shape when only three classes are used? Explain why this
shape results What does this exercise tell you about relying on a histogram to
draw inferences about the shape of the population of values from which the
sample was obtained?
Solution:
(simulation exercise by student which shows that histograms are not
reliable indicators for the shape of population distributions)
, METHODS OF COLLECTING AND PRESENTING DA TA 7
1.15. Explain why consecutive observations that are correlated will be apparent
from a digidot plot but not from a dotplot, histogram, stem-and-leaf display,
scatter plot, or boxplot. Is there another plot that you would recommend for
detecting this type of correlation? Explain.
Solution:
There is no time order involved in a dotplot, histogram, stem-and-leaf display,
scatter plot, or boxplot. A time sequence plot would be another possibility.
1.17. Construct a box plot of your driving times from the previous problem. Do
any of your times show as an outlier? If the box doesn't exhibit approximate
symmetry, try to provide an explanation for the asymmetry.
Solution:
(box plot to be individually constructed using the student driving data from
Exercise 1.16)
1.19. Given in file NBA2003.MTW are the scoring averages for the top 25 scorers
in the National Basketball Association (NBA) in 2002. The data are given below
Name Scoring Average
1 Tracy McGrady 32.1
2 Kobe Bryant 30.0
3 Allen Iverson 27.6
4 Shaquille O'Neal 27.5
5 Paul Pierce 25.9
6 Dirk Nowitzki 25.1
7 Tim Duncan 23.3
8 Chris Webber 23.0
9 Kevin Garnett 23.0
10 Ray Allen 22.5
11 Allan Houston 22.5
12 Stephon Marbury 22.3
13 Antawn Jamison 22.2
14 Jalen Rose 22.1
15 Jamal Mashburn 21.6
16 Jerry Stackhouse 21.5
17 Shawn Marion 21.2
18 Steve Francis 21.0
19 Glenn Robinson 20.8
20 Jermaine O'Neal 20.8
21 Ricky Davis 20.6
22 Karl Malone 20.6
23 Gary Payton 20.4
24 Antoine Walker 20.1
25 Michael Jordan 20.0
What type of graphical display would you recommend for displaying the data?
Construct the display, but before doing so, would you expect the averages to
exhibit asymmetry? Why or why not?
, * METHODS OF COLLECTING AND PRESENTING DA TA
Solution:
A dotplot, given below, would be a reasonable way to display the data. We would
expect the data to display right skewness as we would expect to see more scoring
averages below the median of the top 25 than above the median.
1.21. With a conventional scatter plot, two variables are displayed — one on the
vertical axis and one on the horizontal axis. How many variables were displayed
in the scatter plot in Figure 1.5? Can you think of how additional variables might
be displayed?
Solution:
Three variables were displayed in Figure 1.5. A fourth variable could be displayed
by having a separate graph for each value ofthat variable. And so on.
1.23. A data set contains 25 observations. The median is equal to 26.8, the range
is 62, Q\ = 16 7, and Q% = 39.8. What is the numerical value of the interquartile
range?
Solution:
The interquartile range is Qs - Q\ 39.8 - 16.7 = 23.1
1.25. Would a histogram of the data given in Exercisel.l be a meaningful display?
Why or why not?
Solution:
No, a histogram would not be particularly useful. Since the data are obtained over
time, a display that incorporates time should be used
SOLUTIONS MANUAL
,Contents
1 Methods of Collecting and Presenting Data 1
2 Measures of Location and Dispersion 27
3 Probability and Common Probability Distributions 37
4 Point Estimation 51
5 Confidence Intervals and Hypothesis Tests—One Sample 59
6 Confidence Intervals and Hypothesis Tests—Two Samples 73
7 Tolerance Intervals and Prediction Intervals 83
8 Simple Linear Regression, Correlation and Calibration 87
9 Multiple Regression 101
10 Mechanistic Models 117
11 Control Charts and Quality Improvement 121
12 Design and Analysis of Experiments 139
13 Measurement System Appraisal 155
14 Reliability Analysis and Life Testing 157
15 Analysis of Categorical Data 163
16 Distribution-Free Procedures 171
17 Tying It All Together 175
, Modern Engineering Statistics: Solutions Manual to Accompany
by Thomas P. Ryan
Copyright © 2007 John Wiley & Sons, Inc.
/
Methods of Collecting and Presenting Data
Note: The data in the following exercises, including data in MIN1TABfiles(i.e.,
the files with the MTW extension), can be found at the website for the text:
ftp://ftp.wiley.com/public/sci_tech med/engineeringstatistics. This also applies to
the other chapters in the text.
1.1. Given below are the earned run averages (ERAs) for the American League for
1901-2003 (in ERAMC MTW), with the years 1916 and 1994 corrected from the
source, Total Baseball, 8th edition, by John Thorn, Phil Birnbaum, and Bill
Deane, since those two years were obviously in error. (The league started in
1901.)
Year 1901 1902 1903 1904 1905 1906 1907 1908
1909 1910 1911 1912 1913 1914
ERA 3.66 3.57 2.96 2.60 2.65 2.69 2.54 2.39
2.47 2.51 3.34 3.34 2.93 2.73
Year 1915 1916 1917 1918 1919 1920 1921 1922
1923 1924 1925 1926 1927 1928
ERA 2.93 2.82 2.66 2.77 3.22 3.79 4.28 4.03
3.98 4.23 4.39 4.02 4.14 4.04
Year 1929 1930 1931 1932 1933 1934 1935 1936
1937 1938 1939 1940 1941 1942
ERA 4.24 4.64 4.38 4.48 4.28 4.50 4.45 5.04
4.62 4.79 4.62 4.38 4.15 3.66
Year 1943 1944 1945 1946 1947 1948 1949 1950
1951 1952 1953 1954 1955 1956
ERA 3.29 3.43 3.36 3.50 3.71 4.29 4.20 4.58
4.12 3.67 3.99 3.72 3.96 4.16
Year 1957 1958 1959 1960 1961 1962 1963 1964
1965 1966 1967 1968 1969 1970
ERA 3.79 3.77 3.86 3.87 4.02 3.97 3.63 3.62
3.46 3.43 3.23 2.98 3.62 3.71
Year 1971 1972 1973 1974 1975 1976 1977 1978
1979 1980 1981 1982 1983 1984
ERA 3.46 3.06 3.82 3.62 3.78 3.52 4.06 3.76
4.21 4.03 3.66 4.07 4.06 3.99
Year 1985 1986 1987 1988 1989 1990 1991 1992
1993 1994 1995 1996 1997 1998
ERA 4.15 4.17 4.46 3.96 3.88 3.90 4.09 3.94
4.32 4.80 4.71 5.00 4.57 4.65
Year 1999 2000 2001 2002 2003
ERA 4.86 4.91 4.47 4.46 4.52
/
, 2 METHODS OF COLLECTING AND PRESENTING DA TA
Construct a time sequence plot, either by hand or using software such as
MTNITAB, or equivalently a scatterplot with ERA plotted against Year. Does the
plot reveal a random pattern about the overall average for these 103 years, or does
the plot indicate nonrandomness and/or a change in the average?
Solution:
Here is the time sequence plot that is actually in the form of a scatterplot.
(a) There is considerable nonrandomness in this plot, especially the strong
upward trend since about 1970 as well as the monotonicity during certain intervals
of years (e.g., strictly decreasing from 1938-43.)
1.3. Construct a dotplot for the data in Example 12
Solution:
, METHODS OF COLLECTING AND PRESENTING DA TA 3
1.5. Statistical literacy is important not only in engineering but also simply as a
means of expression. There are many statistical guffaws that appear in lay
publications. Some of these are given in the "Forsooth" section of RSS News
(Royal Statistical Society News) each month. Others can be found online at
Chance Nws, whose website is at the following URL:
http://www.dartmouth.edu/~chance/chance_news/news.html. The following two
statements can be found at the latter website. Explain what is wrong with each
statement.
(a) Migraines affect approximately 14% of women and 7% of men, that's one-
fifth the population (Herbal Health Newsletter Issue I)
(b) Researchers at Cambridge University have found that supplementing with
vitamin C may help reduce the risk of death by as much as 50% (Higher Nature
Health News No. HN601, 2001).
(Comment: Although the errors in these two statements should be obvious,
misstatements involving statistical techniques are often made, even in statistics
books, that are not obvious unless one has a solid grasp of statistics )
Solution:
(a) The percentages are not additive since neither is based on 100% of the
population of men and women combined. More specifically, even if the number of
women was the same as the number of men, the base would be doubled if the
populations were combined, rather than staying at the common number, as would
be necessary for the percentages to be additive.
,4 METHODS OF COLLECTING AND PRESENTING DA TA
(b) The risk will always be 100% ... regardless of the amount of Vitamin C that
is ingested!
1.7. Consider Figure 1.5. The data are as follows (in 75-25PERCENTILES2002.MTW):
SAT 75th a c c e p t a n c e SAT 25th
Row percentile rate percentile
1 1540 12 1350
2 1580 11 1410
3 1550 16 1380
4 1580 13 1450
5 1560 16 1410
6 1560 13 1360
7 1490 23 1310
8 1500 26 1300
9 1510 13 1310
10 1520 21 1330
11 1490 44 1280
12 1470 33 1290
13 1510 23 1310
14 1450 30 1290
15 1490 16 1290
16 1480 32 1300
17 1460 45 1300
18 1460 31 1270
19 1430 34 1270
20 1450 26 1200
21 1410 39 1200
22 1400 55 1220
23 1460 36 1280
24 1400 29 1170
25 1380 49 1220
26 1410 26 1240
27 1340 37 1130
28 1410 41 1230
29 1370 38 1160
30 1450 22 1280
31 1420 29 1250
32 1420 48 1220
33 1400 34 1210
34 1410 50 1240
35 1390 32 1220
36 1450 71 1240
37 1365 46 1183
38 1420 57 1250
39 1290 63 1060
40 1275 57 1070
41 1330 79 1130
42 1270 78 1050
43 1290 48 1080
44 1350 36 1150
45 1370 73 1180
46 1290 66 1070
47 1290 47 1090
48 1310 62 1090
49 1390 73 1210
, METHODS OF COLLECTING AND PRESENTING DA TA S
(a) Construct the graph of the acceptance rate against the 75th percentile SAT
score with the latter on the horizontal axis. Is the slope exactly the same as the
slope of Figure 1.5? Explain why the slope should or should not be the same.
(b) Construct the graph of the 25th percentile SAT score against the acceptance
rate with the former on the vertical axis. (The data on the 25th percentile are in
the third column in the file.) Does the point that corresponds to point #22 in
Figure 1.5 also stand out in this graph?
(c) Compute the difference between the 75th percentile and 25th percentile for
each school and plot those differences against the acceptance rate. Note that
there are two extreme points on the plot, with differences of 250 and 130,
respectively One of these schools is for a prominent public university and the
other is a private university, both in the same state. Which would you guess to be
the public university?
Solution:
(a) No, the slopes (of a line fit through the points, for example) will not be the
same because the axes are reversed.
(b) No, there are no points on the graph that stand out as being unusual.
(c) We would guess that the point with the higher acceptance rate would be the
public university (which it is: University of California —Berkeley)
1.9. Consider different amounts of one-dimensional data. What graphical display
would you recommend for each of the following numbers of observations: (a) 10,
(b) 100, and (c) 1000?
Solution:
(a) dotplot (b) dotplot or histogram (c) histogram
1.11. The following numbers are the first 50 of 102 chemical data measurements
of color from a leading chemical company that were given in Ryan (2000): 0.67,
0.63, 0.76, 0.66, 0.69, 0.71, 0.72, 0.71, 0.72, 0.72, 0.83, 0.87, 0.76, 0.79, 0.74,
0.81, 0.76, 0.77, 0.68, 0.68, 0.74, 0.68, 0.68, 0.74, 0.68, 0.69, 0.75, 0.80, 0.81,
0.86, 0.86, 0.79, 0.78, 0.77, 0.77, 0.80, 0.76, 0.67, 0.73, 0.69, 0.73, 0.73, 0.74,
0.71, 0.65, 0.67, 0.68, 0.71, 0.69, and 0.73.
(a) What graphical display would you suggest if it was suspected that there may
be some relationship between consecutive measurements (which would violate one
of the assumptions of the statistical methods presented in later chapters)?
(b) Construct the display that you suggested in part (a). Do consecutive
observations appear to be related?
, 6 METHODS OF COLLECTING AND PRESENTING DA TA
Solution:
(a) Time sequence plot or autocorrelation plot, preferably the latter.
(b) The autocorrelation function plot (the correlation between units one unit
apart, two units apart...) is given below. There does appear to be autocorrelation,
especially of observations one or two units apart since the autocorrelations for the
first two lags are above the upper decision line (95% confidence interval) and the
/-statistics exceed 2, as can be seenfromthe numbers below the graph.)
Autocorrelation Function for C1
10
c ~
o _
06 _
(0 0<
02 -
<D
00
-
t
o
o
-0?
_
o ■ 04
~
■ •=!
-08 ~
< -10 ~
~ "i ~\—■ r
2 7 12
Lag Con T LBQ Lag Corr T LBQ
1 058 411 1795 8 -034 -155 4389
2 042 230 27 56 9 -0.36 -157 5201
3 0.31 153 32 79 10 -0 46 -194 65 86
4 017 081 3443 11 -0.37 -1.46 75.10
5 0 06 0 30 3466 12 -0 23 -0 86 7866
6 -0 02 -011 3469
7 -019 -0 89 36 88
1.13. This exercise illustrates how the choice of the number of intervals greatly
influences the shape of a histogram. Construct a histogram of the first 100
positive integers for the following numbers of classes: 3, 4, 6, 7, 10, and 12. (The
number of classes can be specified in MINITAB, for example, by using the NINT
subcommand with the HIST command, and the sequence MTB>SET Cl,
DATA>1:100, DATA>END will place the first 100 integers in the first column of
the worksheet.) We know that the distribution of numbers is uniform over the
integers 1-100 because we have one of each. We also have the same number of
observations in the intervals 1-9, 10-19, 20-29, and so on. Therefore, the
histograms should theoretically be perfectly flat Are any of the histograms flat?
In particular, what is the shape when only three classes are used? Explain why this
shape results What does this exercise tell you about relying on a histogram to
draw inferences about the shape of the population of values from which the
sample was obtained?
Solution:
(simulation exercise by student which shows that histograms are not
reliable indicators for the shape of population distributions)
, METHODS OF COLLECTING AND PRESENTING DA TA 7
1.15. Explain why consecutive observations that are correlated will be apparent
from a digidot plot but not from a dotplot, histogram, stem-and-leaf display,
scatter plot, or boxplot. Is there another plot that you would recommend for
detecting this type of correlation? Explain.
Solution:
There is no time order involved in a dotplot, histogram, stem-and-leaf display,
scatter plot, or boxplot. A time sequence plot would be another possibility.
1.17. Construct a box plot of your driving times from the previous problem. Do
any of your times show as an outlier? If the box doesn't exhibit approximate
symmetry, try to provide an explanation for the asymmetry.
Solution:
(box plot to be individually constructed using the student driving data from
Exercise 1.16)
1.19. Given in file NBA2003.MTW are the scoring averages for the top 25 scorers
in the National Basketball Association (NBA) in 2002. The data are given below
Name Scoring Average
1 Tracy McGrady 32.1
2 Kobe Bryant 30.0
3 Allen Iverson 27.6
4 Shaquille O'Neal 27.5
5 Paul Pierce 25.9
6 Dirk Nowitzki 25.1
7 Tim Duncan 23.3
8 Chris Webber 23.0
9 Kevin Garnett 23.0
10 Ray Allen 22.5
11 Allan Houston 22.5
12 Stephon Marbury 22.3
13 Antawn Jamison 22.2
14 Jalen Rose 22.1
15 Jamal Mashburn 21.6
16 Jerry Stackhouse 21.5
17 Shawn Marion 21.2
18 Steve Francis 21.0
19 Glenn Robinson 20.8
20 Jermaine O'Neal 20.8
21 Ricky Davis 20.6
22 Karl Malone 20.6
23 Gary Payton 20.4
24 Antoine Walker 20.1
25 Michael Jordan 20.0
What type of graphical display would you recommend for displaying the data?
Construct the display, but before doing so, would you expect the averages to
exhibit asymmetry? Why or why not?
, * METHODS OF COLLECTING AND PRESENTING DA TA
Solution:
A dotplot, given below, would be a reasonable way to display the data. We would
expect the data to display right skewness as we would expect to see more scoring
averages below the median of the top 25 than above the median.
1.21. With a conventional scatter plot, two variables are displayed — one on the
vertical axis and one on the horizontal axis. How many variables were displayed
in the scatter plot in Figure 1.5? Can you think of how additional variables might
be displayed?
Solution:
Three variables were displayed in Figure 1.5. A fourth variable could be displayed
by having a separate graph for each value ofthat variable. And so on.
1.23. A data set contains 25 observations. The median is equal to 26.8, the range
is 62, Q\ = 16 7, and Q% = 39.8. What is the numerical value of the interquartile
range?
Solution:
The interquartile range is Qs - Q\ 39.8 - 16.7 = 23.1
1.25. Would a histogram of the data given in Exercisel.l be a meaningful display?
Why or why not?
Solution:
No, a histogram would not be particularly useful. Since the data are obtained over
time, a display that incorporates time should be used
