Preview Extract

Chapter 2: Graphical Summaries of Data
15. (A)
Section 2.1 Exercises
Exercises 1 โ 4 are the Check Your
Understanding exercises located within
the section. Their answers are found on
pages 48 and 49.
(B)
Understanding the Concepts
5.
6.
7.
8.
9.
frequency
relative frequency
Pareto chart
pie chart
False. In a frequency distribution, the sum
of all frequencies equals the total number
of observations.
10. True
11. True
12. False. In bar graphs and Pareto charts, the
heights of the bars represent the
frequencies or relative frequencies.
(C) Everyone (E)
(D) False
(E) True (12.5% < 20%)
16. (A)
(B)
Practicing the Skills
13. (A) Meat, poultry, fish, and eggs
(B) False ($450 $1000)
14. (A) Type O
(B) False (
70
= 46.7% )
150
(C) Medicare and Medicaid
(D) 68.8% (27.7% + 25.1% + 9.6% +
6.4%)
(C) True
17. (A) West, South
(B) Northeast, Midwest
(C) True
(D) False (the Northeast had around
18%)
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consent of McGraw-Hill Education.
18. (A) The game
(B) True
(C) False (men < women)
(D) True (both are about 0.65)
20. (A)
19. (A)
(B)
(B)
(C)
(D) True,
7.2
= 0.324
22.2
21. (A)
(C)
(D) True
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consent of McGraw-Hill Education.
(B)
22. (A)
(B)
(C)
(C)
(D)
(D)
(E)
(E)
(F) False. 28.9% 50%.
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consent of McGraw-Hill Education.
23. (A)
24. (A)
(B)
(B)
(C)
(C)
(D)
(E)
(D)
(F) True. (3800 > 3134)
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consent of McGraw-Hill Education.
(E)
(C)
(D)
(F) True. 62.1% > 50%
(G) False. 10.8% 50%)
(F) True. 43.9% are females
(G) 0.289
(B)
26. (A)
(B)
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consent of McGraw-Hill Education.
(C)
(D)
(D)
(E) True. 30.5% never back up their
data.
(F) False. 54.2% > 50%.
28. (A)
(E) True. (64.5% > 50%)
(F) 0.106
27. (A)
(B)
(B)
(C)
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consent of McGraw-Hill Education.
(C)
(B)
(C)
(D)
(D)
(E)
(E) 0.210
30. (A)
(F) 0.132
29. (A)
(B)
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consent of McGraw-Hill Education.
(C)
32. (A)
(D) False. Download album increased.
(B)
31. (A)
(B)
(C)
(C)
(D)
(D) True
(E) True. 46.5 > 41.1
(E) 0.132
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33. (A)
(E) True. 167.9 > 156.
34. This is not a valid relative frequency
distribution because the proportions do
not sum to 1.
Extending the Concepts
(B)
35. (A)
(C)
(B)
(D)
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consent of McGraw-Hill Education.
(C)
Section 2.2 Exercises
Exercises 1-4 are the Check Your
Understanding exercises located within
the section. Their answers are found on
page 68.
Understanding the Concepts
(D)
(E) The total frequency is equal to the
sum of the frequencies for the two
cities.
(F) The total relative frequency is the
total frequency divided by the sum of
all total frequencies. The relative
frequency for each city is the
frequency for that city divided by the
sum of the frequencies for that city.
Since the sum of the frequencies for
each city is not the same as the sum of
the total frequencies, the total relative
frequency is not the sum of the
relative frequencies for the two cities.
36.(A) No. The proportions are not parts of
a whole. In particular, they do not add
up to 1.
(B) No. This is not a frequency table.
5.
6.
7.
8.
9.
symmetric
left, right
bimodal
cumulative frequency
False. In a frequency distribution, the
class width is the difference between
consecutive lower class limits.
10. False. The number of classes used has
a large effect on the shape of the
histogram.
11. True
12. True
Practicing the Skills
13. Skewed to the left
14. Skewed to the right
15. Approximately symmetric
16. Approximately symmetric
17. Bimodal
18. Unimodal
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Working with the Concepts
19. (A) 11
(B) 1
(C) 70-71
(D) 9%
(E) Approximately symmetric
20. (A) 3
(B) 19
(C) 3
(D) Skewed to the right
21. (A) The sum of the proportions in the
last 5 rectangles yields the percentage
of men with levels above 240. This
sum is closest to 30%.
(B) 240-260
22. (A) The sum of the proportions in the
last 8 rectangles yields the percentage
of women with pressures above 120.
The sum is closest to 50%.
(B) 130-135
23. (A) False
(B) True
(C) 9
(D) No
(E) Skewed to the right.
24. (A) 50 – 55
(B) 30%
(C) 60 โ 70
25. (A) Right skewed, because there are
more words of small length than of
larger length.
(B) Left skewed, because there are
more coins in circulation from recent
years than older years.
(C) Left skewed, because there are
more high grades than low ones.
26. (A) Right skewed, because there are
more people with low incomes than
high.
(B) Left skewed, because there are
more students finishing the exam
close to the allotted 60 minutes.
(C) Right skewed, because there are
more people with younger ages than
older.
27. (A) 9
(B) 0.020
(C) Lower limits: 0.180, 0.200, 0.220,
0.240, 0.260, 0.280, 0.300, 0.320, 0.340.
Upper limits: 0.199, 0.219, 0.239,
0.259, 0.279, 0.299, 0.319, 0.339, 0.359.
(D)
(E)
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consent of McGraw-Hill Education.
(F)
(G) 0.109 + 0.037 + 0.004 = 0.15 = 15%
(H) 0.015 + 0.052 = 0.067 = 6.7%
28. (A)
(D)
(E)
(F)
(B)
(C)
(G) 0.097 + 0.04 = 0.137 = 13.7%
(H) 0.119 + 0.035 + 0.007 = 0.161 =
16.1%
(I) Batting averages tend to be a bit
higher in the National League.
29. (A) 10
(B) 3.0
(C) The lower class limits are 1.0, 4.0,
7.0, 10.0, 13.0, 16.0, 19.0, 22.0, 25.0,
and 28.0. The upper class limits are
3.9, 6.9, 9.9, 12.9, 15.9, 18.9, 21.9, 24.9,
27.9, and 30.9.
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consent of McGraw-Hill Education.
(D)
(D)
(E)
(E)
(F)
(G) 0.125 + 0.17 + 0.24 = 0.535 =
53.5%
(H) 0.065 + 0.035 + 0.015 + 0.005 =
0.12 = 12.0%
30. (A) 11
(B) 5
(C) The lower class limits are 0.0, 5.0,
10.0, 15.0, 20.0, 25.0, 30.0, 35.0, 40.0,
45.0, and 50.0. The upper class limits
are 4.9, 9.9, 14.9, 19.9, 24.9, 29.9, 34.9,
39.9, 44.9, 49.9, and 54.9.
(F)
(G) 0.288 + 0.315 = 0.603 = 60.3%
(H) 0.027 + 0.027 + 0.027 = 0.081 = 8.1%
31. (A)
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consent of McGraw-Hill Education.
(B)
(C)
(D)
(G) Both are reasonably good choices
for class widths. The number of
classes are both at least 5, but less than
20. Also, neither class widths are too
narrow or too wide.
32. (A)
(E) Unimodal
(F)
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consent of McGraw-Hill Education.
(B)
(C)
(D)
(E) Skewed to the left
(G) Answers will vary. The class width of
5 provides a more appropriate level of
detail in the middle of the histogram,
but is very sparse in the tails. The class
width of 10 is better in the tails, but
most of the data are in only two
classes.
33. (A) Answers will vary. Here is one
possibility:
(F)
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consent of McGraw-Hill Education.
(B)
(G)
(C) Answers will vary. Here is one
possibility:
(D)
(E) Skewed to the right
(F) Answers will vary. Here is one
possibility:
(H) The one with 9 classes is more
appropriate than the one with only 5
classes. This is because the one with
only 5 classes is too wide. Only the
most basic features of the data are
visible.
34. (A)
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consent of McGraw-Hill Education.
(B)
(G)
(C)
(D)
(H) The graphs with nine classes are
much more appropriate than those
with only 4 classes. This is because
only the most basic features of the
data are visible, when the class widths
are too wide, as they are in the graphs
containing only four classes.
35. (A)
(E) Skewed to the right
(F) Answers will vary. Here is one
possibility:
(B)
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consent of McGraw-Hill Education.
(C) Skewed to the right
(B)
36. (A)
40. (A)
(B)
(B)
(C) Skewed to the left
37. Histogram B represents death from
accidents. People who die from accidents
tend to be younger than those who die
from natural causes.
(C)
38. There is a gap between the top 15
scores and all of the others.
39. (A)
(D)
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consent of McGraw-Hill Education.
41. (A)
43. (A)
(B)
(B)
42. (A)
(C)
(B)
(D)
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consent of McGraw-Hill Education.
44. (A)
(E)
(B)
(F)
(C)
(G)
(D)
(H)
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consent of McGraw-Hill Education.
45. (A)
46. (A)
(B)
(B)
(C)
(C)
(D)
(D)
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consent of McGraw-Hill Education.
47. It is not possible to construct a histogram
for this data set because โ30 or moreโ
represents an open ended class.
(D)
48. Yes. The last class would become 3034.9.
Extending the Concepts
49. We solve the following equation:
0.2 + 0.3 + 0.15 + x + 0.1 + 0.1 = 1
Answer: x = 0.15
50. (A) The respective class widths are 1,
0.5, 0.5, 1, 1, and 3.
(B)
(E) Dividing the relative frequency by the
class width adjusts for the differing widths
of the classes.
51. (i) is skewed and (ii) is approximately
symmetric
52. Skewed to the right because the first
two classes have relative frequencies of 0.2
and 0.37. The other classes are all less
than 0.15.
53. A and B are correct, but C is incorrect.
Section 2.3 Exercises
This histogram gives a distorted
picture of the data because it makes it
look like this is a bimodal distribution,
when in reality, Figure 2.6 shows that
the data has one mode and is skewed
to the right.
(C)
Exercises 1 and 2 are the Check Your
Understanding exercises located within
the section. Their answers are found on
page 80.
Understanding the Concepts
3.
4.
5.
6.
7.
8.
leaf
stems
time-series plot
time
True
False. In a stem-and-leaf plot, each leaf
must be a single digit.
9. True
10. False. In a time-series plot, the horizontal
axis represents time.
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consent of McGraw-Hill Education.
Practicing the Skills
(B)
11.
12.
13. The list is: 30 30 31 32 35 36 37 37 39
42 43 44 45 46 47 47 47 47 48 48 49 50 51
51 51 52 52 52 52 54 56 57 58 58 59 61 63
14. The list is: 14.4 14.6 14.8 14.9 15.1 15.2
15.2 15.4 15.5 15.7 15.7 15.8 16.0 16.1 16.1
16.1 16.2 16.3 16.7 16.7 16.9 18.2 18.3 18.8
15.
16.
(C) The one in part (A) is more
appropriate because part (B) has too
many stems with no leaves. The stemand-leaf plot in part (A) shows that
most prices are in the 30โs, 40โs, and
50โs, and that the data is skewed to the
right.
Working with the Concepts
18. (A)
17. (A)
(B)
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consent of McGraw-Hill Education.
(C) The one in part (B) is more
appropriate because most of the leaves
are on three stems (temperatures in
the 50โs, 60โs, and 70โs). For this
reason, the stem-and-leaf plot in part
(A) does not reveal much detail about
the data.
19. (A)
21. (A)
(B) Leaf 1 represents the ages of the
Wimbledon winners and Leaf 2
represents the ages of the winners of
the Masterโs. From this back-to-back
split stem-and-leaf plot, we see that
the Wimbledon champions tend to be
younger.
(B) Both plots show that more leaves
are on stem 1 than all other stems.
However, the advantage to the split
stem-and-leaf plot in part (A) is that it
much better shows how the emissions
data is skewed to the right.
22. (A) In the following back-to-back split
stem-and-leaf plot, Leaf 1 displays the
lengths of time of the PG-13 movies
and Leaf 2 does so for the R rated
movies.
20.
(B) They differ greatly. R-rated movies
tend to be shorter.
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consent of McGraw-Hill Education.
23. Yes, there are three small gaps in the
dotplot below for the Macon, GA
temperature data.
24. This dotplot shows that the data is
skewed to the right.
27. (A)
(B) Increased: 1960โs, 1980โs, 2000โs.
Decreased: 1950โs, 1970โs, 1990โs,
2010โs.
(C) It caused a big decrease.
(D) It increased from 1965 to 1969, and
then decreased from 1969 to 1975.
25. (A)
28. (A)
(B) Increasing: 2000โ2003; 2007โ2010.
Decreasing: 1993โ2000; 2003โ2007;
2010โ2016.
26. (A)
(B) Decreasing
(B) Female enrollment is growing faster.
29. (A) $300 billion
(B) Both are about $320 billion.
(C) False. 1997 was about $260 billion.
Double this amount would be $520
billion, and 2014 wasnโt even $400
billion.
(D) It decreased.
30. (A) 1980. As evidenced by 0 gold
medals.
(B) 85
(C) About the same
31. (A) 28
(B) 1990
(C) Greater than
(D) About the same
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consent of McGraw-Hill Education.
32. The number of participating countries
increased between 1952 and 1972.
33. (A) 115 inches
(B) 1910
(C) Less than
(D) True. It occurred in the 1880s.
(E) False.
34. (A) 2007
(B) False. It decreased several
times between 2008 and 2012
(C) The number of three-point shots
made increased, then decreased.
35. (A) 4%
(B) It increased
(C) It decreased
(D) It increased
36. (A) 2007
(B) 2012
(C) False. It was not in 2013.
(D) False. It increased between 2012 and
2013.
(B)
(C) They both have the same shape
(skewed to the right), because the class
width in the histogram is 5, as is each line
for each stem 5. The number of leaves in
each stem is the frequency of occurrence,
which is also the height of the bars in the
histogram.
Section 2.4 Exercises
Exercises 1 and 2 are the Check Your
Understanding exercises located within
the section. Their answers are found on
page 86.
Understanding the Concepts
Extending the Concepts
37. (A)
3. 0
4. proportional
5. (i). Graph (A) presents an accurate
picture, because the baseline is at zero.
Graph (B) exaggerates the decline,
because the baseline is above zero.
6. The bar graph presents a more accurate
picture because its baseline is correctly
placed at 0. The time-series plot
exaggerates the rate of the increase.
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consent of McGraw-Hill Education.
7. Graph (B) presents the more accurate
picture. The baseline is at zero, and the
bars are of equal width. The dollar bill
graphic does not follow the area principle.
The length and width of the smaller image
are about 25% less than the length and
width of the larger image, so the area of
the smaller image is about 50% less than
that of the larger image. This exaggerates
the
difference.
8. Graph (B) presents the more accurate
picture, because it follows the area
principle. In Graph (A), the area of the
larger image is about six times that of the
smaller image. This exaggerates the
difference.
9. The graph is misleading, because the
baseline is not at zero.
10. It presents an accurate picture, because
the baseline is at zero.
11. (A) It is misleading because you can see
the tops of the bars in the threedimensional graph. This often causes
them to look shorter than they really are.
13. (i) is more accurate. The plot on the left
has its baseline at zero, and presents an
accurate picture. The plot on the right
exaggerates the increase.
14. (ii) is more accurate. Time series plot (B),
with the baseline at zero, presents an
accurate picture. Plot (A) exaggerates the
decrease.
Extending the Concepts
15. (A)
(B) It makes the differences look smaller,
because the scale on the y-axis extends
farther than the largest bar height.
(C) Figure 2.23 has a baseline of zero, and
the scale on the y-axis is appropriate
for the bar height.
(B)
Chapter Quiz
1.
12. It is misleading because the baseline is not
placed at zero.
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consent of McGraw-Hill Education.
(B)
2.
3.
8.
4.
9.
5. The classes are: 5.0-7.9, 8.0-10.9, 11.013.9, 14.0- 16.9, and 17.0-19.9. The class
width is 3.
6. True
10. 11 11 15 15 19 19 19 22 22 23 25 27 28 30
30 38 44 45 47 48 50 51 53 53 55 56 58
11.
7. (A)
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consent of McGraw-Hill Education.
2. (A)
12.
(B)
13.
14.
(C) False, 50.95% < 59.2%.
3. (A)
15. Twice
Review Exercises
1. (A) Somewhat
(B) True
(C) False. Roughly 36% believe these
ways, which is less than half.
(D) True
(B) True
(C) The Midwest
4. (A)
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consent of McGraw-Hill Education.
(B)
(E)
(F)
(C) False. 48% is less than half.
5. (A) 7
(B) 10
5
1
=
= 10%
50 10
(D) Unimodal
(C)
6. (A) 8
(B) 20
(C) The lower class limit are 20, 40, 60,
80, 100, 120, 140, and 160. The upper
class limits are 39, 59, 79, 99, 119, 139,
159, and 179.
(D)
(G)
12
= 0.226 = 22.6%
53
(H)
17
= 0.321 = 32.1%
53
7. (A)
(B)
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consent of McGraw-Hill Education.
(C)
(D)
(D)
9.
8. (A)
10. (A)
(B)
(B)
(C)
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consent of McGraw-Hill Education.
(C)
(B)
(D)
(C) The split stems in part (B) provides a
more appropriate level of detail.
11. (A)
12.
13. (A)
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consent of McGraw-Hill Education.
(B)
5. Answers will vary.
Case Study: Do Hybrid Cars Get Better
Gas Mileage?
1.
(C) The number of Pandora subscribers
increased from 2010 to 2015, then
decreased slightly between 2015 and
2016. The number of Spotify
subscribers increased steadily from
2010 to 2016.
14. (A) Highest in 1990, lowest in 1930.
(B) Increasing
(C) Life expectancy has increased.
15. Option (i) is the correct statement. The
second graph is misleading due to the fact
that its baseline does not start at zero.
Write About It
1. A frequency bar graph and the relative
frequency bar graph for the same data are
identical except for the scale on the
vertical axis. This is because the relative
frequency bar graph converts the
frequencies to their corresponding
proportional equivalents.
2. The main difference between frequency
distributions for qualitative and
quantitative data is that there are no
natural categories for quantitative data.
For quantitative data, the data must be
divided into classes
3. Answers will vary.
4. Answers will vary.
2. A class width of two is too narrow for
these data because there are 19 classes,
which is too many for a data set
containing only 56 data values.
3.
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consent of McGraw-Hill Education.
4. The histogram is bimodal with little
skewness.
5. Answers will vary. Here is a frequency
distribution with a class width of 2.
6. Answers will vary. Here is a relative
frequency distribution with a class width
of 2.
7. The relative frequency histogram is
unimodal and skewed to the right.
8. The mileages vary more for the hybrid
cars.
9.
Answers may vary as to which illustrates
the comparison more effectively. The
back-to-back stem-and-leaf plot puts the
data sets next to each other on the same
axis. The histograms arguably illustrate
the outliers more clearly.
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consent of McGraw-Hill Education.

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