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Preview Extract
CHAPTER 2
Displaying Descriptive Statistics
2.1
a) 27 ๏ฝ 128 ๏พ 100 therefore use 7 classes.
b) 29 ๏ฝ 512 ๏พ 300 therefore use 9 classes.
c) 210 ๏ฝ 1,024 ๏พ 1,000 therefore use 10 classes.
d) 211 ๏ฝ 2,048 ๏พ 2,000 therefore use 11 classes.
2.2 26 ๏ฝ 64 ๏พ 50 therefore use 6 classes.
74 ๏ญ 16
Estimated Class Width ๏ฝ
๏ฝ 9.7 ๏ป 10
6
a) 16-25, 26-35, 36-45, 46-55, 56-65, 66-75
b) 16 to under 26, 26 to under 36, 36 to under 46,
46 to under 56, 56 to under 66, 66 to under 76
2.3
Frequency
Number
1
2
3
4
5
Total
6
6
5
4
3
24
Relative
Frequency
0.250
0.250
0.208
0.167
0.125
1.00
Cumulative
Relative
Frequency
0.250
0.500
0.708
0.875
1.00
2.4 25 ๏ฝ 32 ๏พ 30 therefore use 5 classes.
42.8 ๏ญ 13.9
Estimated Class Width ๏ฝ
๏ฝ 5.8 ๏ป 6
5
2-1
Copyright ยฉ2020 Pearson Education, Inc.
2-2 Chapter 2
Frequency
Class
13 to less than 19
19 to less than 25
25 to less than 31
31 to less than 37
37 to less than 43
Total
6
11
4
7
2
30
Relative
Frequency
0.200
0.367
0.133
0.233
0.067
1.00
Cumulative
Relative
Frequency
0.200
0.567
0.700
0.933
1.0
2.5 26 ๏ฝ 64 ๏พ 36 therefore use 6 classes.
$5,927 ๏ญ $162
Estimated Class Width ๏ฝ
๏ฝ $960 ๏ป $1, 000
6
a, b, c)
Frequency
Class
Less than $1,000
$1,000 to less than $2,000
$2,000 to less than $3,000
$3,000 to less than $4,000
$4,000 to less than $5,000
$5,000 to less than $6,000
Total
12
8
3
2
6
5
36
Relative
Frequency
0.333
0.222
0.083
0.056
0.167
0.139
1.000
Cumulative
Relative
Frequency
0.333
0.555
0.638
0.694
0.861
1.000
d) The following histogram was constructed using bins $999, $1,999, $2,999, $3,999, $4,999,
and $5,999.
Copyright ยฉ2020 Pearson Education, Inc.
Displaying Descriptive Statistics 2-3
2.6 25 ๏ฝ 32 ๏พ 25 therefore use 5 classes.
46 ๏ญ 18
Estimated Class Width ๏ฝ
๏ฝ 5.6 ๏ป 6
5
a, b, c)
Frequency
Class
18-23
24-29
30-35
36-41
42-47
Total
2
6
5
5
7
25
Relative
Frequency
0.08
0.24
0.20
0.20
0.28
1.00
Cumulative
Relative
Frequency
0.08
0.32
0.52
0.72
1.00
d) The following histogram was constructed using bins 23, 29, 35, 41, and 47.
Copyright ยฉ2020 Pearson Education, Inc.
2-4 Chapter 2
2.7
a, b, c)
Frequency
Number
0
1
2
3
4
Total
3
21
23
15
8
70
Relative
Frequency
0.043
0.300
0.329
0.214
0.114
1.000
Cumulative
Relative
Frequency
0.043
0.343
0.672
0.886
1.000
d) The following histogram was constructed using bins 0, 1, 2, 3, and 4.
2.8 26 ๏ฝ 64 ๏พ 40 therefore use 6 classes.
76 ๏ญ 19
Estimated Class Width (Current) ๏ฝ
๏ฝ 9.5 ๏ป 10
6
Results would be similar using the laid-off ages.
Class
19 to less than 29
29 to less than 39
39 to less than 49
49 to less than 59
59 to less than 69
69 to less than 79
Bins
28.9
38.9
48.9
58.9
68.9
78.9
Midpoint
24
34
44
54
64
74
Copyright ยฉ2020 Pearson Education, Inc.
Displaying Descriptive Statistics 2-5
An extra bin (18.9) was added to Excel to provide the open-ended class required by PHStat.
a)
b) According to these ogives, it appears that the current workforce is younger than the laid-off
employees. It appears that the laid-off employees may have a case for age discrimination.
2.9 29 ๏ฝ 512 ๏พ 350 therefore use 9 classes.
$349.99 ๏ญ $2.19
Estimated Class Width ๏ฝ
๏ฝ $38.64 ๏ป $40
9
a, b, c)
Frequency
Class
Less than $40
$40 to less than $80
$80 to less than $120
$120 to less than $160
$160 to less than $200
$200 to less than $240
$240 to less than $280
$280 to less than $320
$320 to less than $360
Total
52
103
91
65
15
11
5
5
3
350
Relative
Frequency
0.149
0.294
0.260
0.186
0.043
0.031
0.014
0.014
0.009
1.000
Cumulative
Relative
Frequency
0.149
0.443
0.703
0.889
0.932
0.963
0.977
0.991
1.000
Copyright ยฉ2020 Pearson Education, Inc.
2-6 Chapter 2
d) The following histogram was constructed using bins 39.999, 79.999, 119.999, 159.999,
199.999, 239.999, 279.999, 319.999, and 359.999.
2.10 27 ๏ฝ 128 ๏พ 125 therefore use 7 classes.
83.2 ๏ญ 71.0
Estimated Class Width ๏ฝ
๏ฝ 1.7 ๏ป 2
7
a, b, c)
Frequency
Class
71 to less than 73
73 to less than 75
75 to less than 77
77 to less than 79
79 to less than 81
81 to less than 83
83 to less than 85
Total
5
37
44
31
6
1
1
125
Relative
Frequency
0.040
0.296
0.352
0.248
0.048
0.008
0.008
1.000
Cumulative
Relative
Frequency
0.040
0.336
0.688
0.936
0.984
0.992
1.000
d) The following histogram was constructed using bins 72.99, 74.99, 76.99, 78.99, 80.99, 82.99,
and 84.99.
Copyright ยฉ2020 Pearson Education, Inc.
Displaying Descriptive Statistics 2-7
e) For 68.8% of the days, ocean temps were lower than 77 degrees.
2.11
a, b, c)
Frequency
Category
Google
Yahoo
Bing
Baidu
Other
Total
20
5
2
2
1
30
Relative
Frequency
0.667
0.167
0.067
0.067
0.033
1.000
Cumulative
Relative
Frequency
0.667
0.833
0.900
0.967
1.000
Copyright ยฉ2020 Pearson Education, Inc.
2-8 Chapter 2
d)
2.12
a, b, c)
Frequency
Category
Excellent
Good
Fair
Poor
Total
16
31
8
5
60
Relative
Frequency
0.267
0.517
0.133
0.083
1.000
Cumulative
Relative
Frequency
0.267
0.783
0.917
1.000
d)
e) 78.3% rated their dining experience as either Excellent or Good.
Copyright ยฉ2020 Pearson Education, Inc.
Displaying Descriptive Statistics 2-9
2.13
2.14
Copyright ยฉ2020 Pearson Education, Inc.
2-10 Chapter 2
2.15
2.16
Copyright ยฉ2020 Pearson Education, Inc.
Displaying Descriptive Statistics 2-11
2.17
2.18
2.19 Because all the possible categories appear to be included in the data, a pie chart would be a
good choice to display this data.
Copyright ยฉ2020 Pearson Education, Inc.
2-12 Chapter 2
2.20 Because we are comparing data from a sample of countries over different time periods, a
clustered bar chart would be a good choice to display this data. A stacked bar chart would not be
the best choice because adding the GDPs for 2 time periods that are 10 years apart is not very
meaningful.
2.21
Grade
A
B
C
Total
Female
5
5
2
12
Male
2
7
3
12
Total
7
12
5
24
71% (5/7) of the As were earned by females even though they comprise of 50% (12/24) of the
students in the class. The females appear to have done better grade-wise than the males.
2.22
Rating
1
2
3
4
Total
Darby
0
2
6
7
15
Exton
2
3
7
3
15
Media
3
8
7
2
20
Total
5
13
20
12
50
Darby received 58% (7/12) of the 4-star ratings even though they were only 30% (15/50) of the
surveyed customers. Darby appears to have higher customer satisfaction when compared to the
other two locations.
Copyright ยฉ2020 Pearson Education, Inc.
Displaying Descriptive Statistics 2-13
2.23
7|12345889
8|036677
9|00479
10 | 0 1 7 7
11 | 0 1 1 2 5 6 8
12 | 0 0 2 5 6
13 | 0 4 4 7 9
2.24
10 | 0 2 5 8 8 9
11 | 0 1 2 3 3 4 4 5
12 | 1 1 1 2 3 3 5 6 7 7 9
13 | 0 2 2 6 7 7 7 9
14 | 0 0 2 5 6
15 | 0
2.25 a)
1|36
2|123479
3|57778
4|00123344557889
5|0011224589
6|47
b)
1 (0) | 3
1 (5) | 6
2 (0) | 1 2 3 4
2 (5) | 7 9
3 (0) |
3 (5) | 5 7 7 7 8
4 (0) | 0 0 1 2 3 3 4 4
4 (5) | 5 5 7 8 8 9
5 (0) | 0 0 1 1 2 2 4
5 (5) | 5 8 9
6 (0) | 4
6 (5) | 7
Copyright ยฉ2020 Pearson Education, Inc.
2-14 Chapter 2
2.26 a)
1|788
2|0 1233444556667788889
3|01
b)
1 (5) | 7 8 8
2 (0) | 0 1 2 3 3 4 4 4
2 (5) | 5 5 6 6 6 7 7 8 8 8 8 9
3 (0) | 0 1
2.27 It appears that the number of Netflix subscribers is increasing during this time period.
Copyright ยฉ2020 Pearson Education, Inc.
Displaying Descriptive Statistics 2-15
2.28 There does not appear to be a consistent relationship between the amount of time on the
web site and the order size.
2.29
2.30 26 ๏ฝ 64 ๏พ 40 therefore use 6 classes.
23 ๏ญ 0
Estimated Class Width ๏ฝ
๏ฝ 3.8 ๏ป 4
6
Copyright ยฉ2020 Pearson Education, Inc.
2-16 Chapter 2
a, b, c)
Frequency
Class
0-3
4-7
8-11
12-15
16-19
20-23
Total
8
5
15
3
6
3
40
Relative
Frequency
0.200
0.125
0.375
0.075
0.150
0.075
1.000
Cumulative
Relative
Frequency
0.200
0.325
0.700
0.775
0.925
1.000
d) The following histogram was constructed using bins 3, 7, 11, 15, 19, and 23.
2.31
a, b, c)
Frequency
Cumulative
Relative
Frequency
0.32
0.50
0.64
0.86
0.96
1.00
Relative
Number
Frequency
0
16
0.32
1
9
0.18
2
7
0.14
3
11
0.22
4
5
0.10
5
2
0.04
Total
50
1.00
d) The following histogram was constructed using bins 0, 1, 2, 3, 4, and 5.
Copyright ยฉ2020 Pearson Education, Inc.
Displaying Descriptive Statistics 2-17
e) 50%
2.32 26 ๏ฝ 64 ๏พ 48 therefore use 6 classes.
1,187 ๏ญ 43
Estimated Class Width ๏ฝ
๏ฝ 190.7 ๏ป 200
6
a, b, c)
Frequency
Class
0 to under 200
200 to under 400
400 to under 600
600 to under 800
800 to under 1,000
1,000 to under 1,200
Total
15
13
11
4
4
1
48
Relative
Frequency
0.313
0.271
0.229
0.083
0.083
0.021
1.000
Cumulative
Relative
Frequency
0.313
0.584
0.813
0.896
0.979
1.000
d) The following histogram was constructed using bins 199.9, 399.9, 599.9, 799.9, 999.9, and
1,199.9.
Copyright ยฉ2020 Pearson Education, Inc.
2-18 Chapter 2
2.33 27 ๏ฝ 128 ๏พ 72 therefore use 7 classes.
795 ๏ญ 190
Estimated Class Width ๏ฝ
๏ฝ 86.4 ๏ป 100
7
a, b, c)
Frequency
Class
101-200
201-300
301-400
401-500
501-600
601-700
701-800
Total
2
2
9
15
31
9
4
72
Relative
Frequency
0.028
0.028
0.125
0.208
0.431
0.125
0.056
1.001
Cumulative
Relative
Frequency
0.028
0.056
0.181
0.389
0.820
0.945
1.001
d) The following histogram was constructed using bins 200, 300, 400, 500, 600, 700, and 800.
Copyright ยฉ2020 Pearson Education, Inc.
Displaying Descriptive Statistics 2-19
2.34 25 ๏ฝ 32 ๏พ 30 therefore use 5 classes.
100 ๏ญ 66
Estimated Class Width (Day) ๏ฝ
๏ฝ 6.8 ๏ป 7
5
Results would be similar using the evening grades.
Class
66-72
73-79
80-86
87-93
94-100
Bins
72
79
86
93
100
Midpoint
69
76
83
90
97
An extra bin (65) was added to Excel to provide the open-ended class required by PHStat.
Copyright ยฉ2020 Pearson Education, Inc.
2-20 Chapter 2
a)
b) The evening class grades appear to be noticeably higher than the day class grades.
2.35 29 ๏ฝ 512 ๏พ 300 therefore use 9 classes.
39 ๏ญ ๏จ ๏ญ14 ๏ฉ
Estimated Class Width ๏ฝ
๏ฝ 5.9 ๏ป 6
9
a, b, c)
Frequency
Class
โ14 to under โ8
โ8 to under โ2
โ2 to under 4
4 to under 10
10 to under 16
16 to under 22
22 to under 28
28 to under 34
34 to under 40
Total
6
28
40
58
68
61
27
9
3
300
Relative
Frequency
0.020
0.093
0.133
0.193
0.227
0.203
0.090
0.030
0.010
0.999
Relative
Cumulative
Frequency
0.020
0.113
0.246
0.439
0.666
0.869
0.959
0.989
0.999
Copyright ยฉ2020 Pearson Education, Inc.
Displaying Descriptive Statistics 2-21
d) The following histogram was constructed using bins โ8.1, โ2.1, 3.9, 9.9, 15.9, 21.9, 27.9,
33.9, and 39.9.
e) Approximately 226 out of 300 flights were not late (75.3%).
2.36 a)
Copyright ยฉ2020 Pearson Education, Inc.
2-22 Chapter 2
b)
2.37 27 ๏ฝ 128 ๏พ 100 therefore use 7 classes.
259 ๏ญ 12
Estimated Class Width (Wayne) ๏ฝ
๏ฝ 35.3 ๏ป 40
7
Results would be similar using the Dover data.
Class
1-40
41-80
81-120
121-160
161-200
201-240
241-280
Bins
40
80
120
160
200
240
280
Midpoint
20.5
60.5
100.5
140.5
180.5
220.5
260.5
An extra bin (0) was added to Excel to provide the open-ended class required by PHStat.
a)
Copyright ยฉ2020 Pearson Education, Inc.
Displaying Descriptive Statistics 2-23
b) It appears that the days on the market for homes sold in Wayne are longer than for homes sold
in Dover.
2.38 a)
Copyright ยฉ2020 Pearson Education, Inc.
2-24 Chapter 2
b)
2.39
2.40
Reason
Too long on hold
Not knowledgeable
Not courteous
Hard to understand
Too many transfers
Other
Total
Frequency
47
22
18
15
10
8
120
Relative
Frequency
0.392
0.183
0.150
0.125
0.083
0.067
Cumulative
Relative
Frequency
0.392
0.575
0.725
0.850
0.933
1.000
Copyright ยฉ2020 Pearson Education, Inc.
Displaying Descriptive Statistics 2-25
2.41
Complaint
Seat belts / air bags problems
Engine problems
Fuel System problems
Body / paint problems
Electrical problems
Brakes problems
Drivetrain problems
Transmission problems
Interior accessories problems
Lights problems
Suspension problems
Miscellaneous problems
Windows / windshield
problems
Wheels / hubs problems
Cooling system problems
Exterior accessories problems
Clutch problems
Steering problems
Exhaust system problems
Cumulative
Relative
Relative
Frequency Frequency Frequency
182
0.428
0.428
54
0.127
0.555
40
0.094
0.649
28
0.066
0.715
25
0.059
0.774
23
0.054
0.828
15
0.035
0.864
9
0.021
0.885
7
0.016
0.901
7
0.016
0.918
7
0.016
0.934
6
0.014
0.948
5
5
4
3
3
1
1
0.012
0.012
0.009
0.007
0.007
0.002
0.002
0.960
0.972
0.981
0.988
0.995
0.998
1.000
425
Copyright ยฉ2020 Pearson Education, Inc.
2-26 Chapter 2
2.42
Copyright ยฉ2020 Pearson Education, Inc.
Displaying Descriptive Statistics 2-27
2.43
2.44
2.45 A bar chart would be appropriate for categorical data. The time data needs to be converted
to common units (minutes).
Copyright ยฉ2020 Pearson Education, Inc.
2-28 Chapter 2
2.46 A clustered bar chart would be appropriate for this data. A stacked bar chart would also be
an option.
2.47 A pie chart is the best choice for this data. The pie chart best illustrates the dominant
position of Android.
Copyright ยฉ2020 Pearson Education, Inc.
Displaying Descriptive Statistics 2-29
2.48 A pie chart is the best choice because all categories are included and the percentage sums to
100%.
2.49 A bar chart, either horizontal or vertical, is the best choice for this data.
Copyright ยฉ2020 Pearson Education, Inc.
2-30 Chapter 2
2.50 A bar chart is the best display for qualitative data organized in categories.
2.51 A bar chart is the best display for quantitative data organized in categories.
Copyright ยฉ2020 Pearson Education, Inc.
Displaying Descriptive Statistics 2-31
2.52 Pie charts are a good choice for displaying qualitative data when the proportions add to
100%.
2.53 A stacked bar chart is the best choice to compare totals from different groups.
2.54 26 ๏ฝ 64 ๏ณ 55 therefore use 6 classes.
66 ๏ญ 26
Estimated Class Width ๏ฝ
๏ฝ 6.7 ๏ป 7
6
Copyright ยฉ2020 Pearson Education, Inc.
2-32 Chapter 2
a, b, c)
Frequency
Class
26-32
33-39
40-46
47-53
54-60
61-67
Total
11
10
16
12
4
2
55
Relative
Frequency
0.200
0.182
0.291
0.218
0.073
0.036
1.00
Cumulative
Relative
Frequency
0.200
0.382
0.673
0.891
0.964
1.00
d) The following histogram was constructed using bins 32, 39, 46, 53, 60 and 67.
Copyright ยฉ2020 Pearson Education, Inc.
Displaying Descriptive Statistics 2-33
2.55 A pie chart is the best choice because the probabilities add to 100%.
2.56 a, b, c)
Frequency
Class
0
1
2
3
4
5
6
7
Total
2
1
13
16
11
10
4
3
60
Relative
Frequency
0.033
0.017
0.217
0.267
0.183
0.167
0.067
0.050
1.001
Cumulative
Relative
Frequency
0.033
0.050
0.267
0.554
0.717
0.884
0.951
1.001
Copyright ยฉ2020 Pearson Education, Inc.
2-34 Chapter 2
d) The following histogram was constructed using bins 0, 1, 2, 3, 4, 5, 6 and 7.
2.57 a)
6|47799
7|000111456778
8|123567789
9|0015678
10 | 2 4
11 | 7
b)
6 (0) | 4
6 (5) | 7 7 9 9
7 (0) | 0 0 0 1 1 1 4
7 (5) | 5 6 7 7 8
8 (0) | 1 2 3
8 (5) | 5 6 7 7 8 9
9 (0) | 0 0 1
9 (5) | 5 6 7 8
10 (0) | 2 4
10 (5) |
11 (0) |
11 (5) | 7
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Displaying Descriptive Statistics 2-35
2.58 As the number of household members increase, the average monthly food costs also tend to
increase.
2.59
Copyright ยฉ2020 Pearson Education, Inc.
2-36 Chapter 2
2.60
2.61
a, b, c)
Frequency
Category
Cheez-Its
Cheese Nips
No Prefer
Total
16
5
3
24
Relative
Frequency
0.667
0.208
0.125
1.000
Cumulative
Relative
Frequency
0.667
0.875
1.000
2.62
1|2358
2|11366778
3|0335669
4|00224679
5|017
Copyright ยฉ2020 Pearson Education, Inc.
Displaying Descriptive Statistics 2-37
2.63
2.64
Brand
Coke
Mt. Dew
Pepsi
Total
Diet
6
2
4
12
Regular
6
8
7
21
Total
12
10
11
33
50% (6/12) of the Coke customers preferred Diet even though only 36% (12/33) of all the
customers prefer Diet soda. Coke customers appear to have a higher percentage of customers
who prefer diet soda than other brands.
2.65
Age
20-29
30-39
40-49
50-59
Total
Callaway
4
9
16
3
32
Nike
2
15
6
3
26
Taylor Made
19
10
8
5
42
Total
25
34
30
11
100
Younger golfers seem to prefer Taylor Made clubs while older golfers seem to refer Callaway.
Copyright ยฉ2020 Pearson Education, Inc.
2-38 Chapter 2
2.66 a)
1|899
2|0002233555688889
3|011112235556699
4|13356
5|1
b)
1 (5) | 8 9 9
2 (0) | 0 0 0 2 2 3 3
2 (5) | 5 5 5 6 8 8 8 8 9
3 (0) | 0 1 1 1 1 2 2 3
3 (5) | 5 5 5 6 6 9 9
4 (0) | 1 3 3
4 (5) | 5 6
5 (0) | 1
2.67 a)
7|0022456777
8|1258
9|0122333457799
10 | 0 1 2 4 5
11 | 2 8 9
12 | 5
13 | 0 0 1 8
b)
7 (0) | 0 0 2 2 4
7 (5) | 5 6 7 7 7
8 (0) | 1 2
8 (5) | 5 8
9 (0) | 0 1 2 2 3 3 3 4
9 (5) | 5 7 7 9 9
10 (0) | 0 1 2 4
10 (5) | 5
11 (0) | 2
11 (5) | 8 9
12 (0) |
12 (5) | 5
13 (0) | 0 0 1
13 (5) | 8
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Displaying Descriptive Statistics 2-39
2.68
There does appear no more than a very weak, positive relationship between payroll and wins
during the 2017 season.
2.69
Copyright ยฉ2020 Pearson Education, Inc.
2-40 Chapter 2
The trend in gasoline prices was a consistent rise until the crisis in 2008. After that crisis,
gasoline prices returned to the high levels of around $3.5 during 2011 to 2014. In 2014 and 2105,
prices fell down to $2.00, with a modest rise afterwards.
2.70
a)
Status
Airline
Delta
Southwest
United
Total
Late
5
5
7
17
On Time
38
22
23
83
Total
43
27
30
100
On Time
0.38
0.22
0.23
0.83
Total
0.43
0.27
0.30
1.00
b)
Status
Airline
Delta
Southwest
United
Total
Late
0.05
0.05
0.07
0.17
c) Delta has the highest on-time percentage (38/43 = 0.88) while United has the lowest (23/30 =
0.77)
2.71
Using Chicago data, 26 ๏ฝ 64 ๏พ 60 therefore use 6 classes.
85 ๏ญ 1
Estimated Class Width ๏ฝ
๏ฝ 14.0 ๏ป 15
6
Class
0 to less than 15
15 to less than 30
30 to less than 45
45 to less than 60
60 to less than 75
75 to less than 90
Bins
14.9
29.9
44.9
59.9
74.9
89.9
Midpoint
7.5
22.5
37.5
52.5
67.5
82.5
An extra bin (โ0.1) was added to Excel to provide the open-ended class required by PHStat.
Copyright ยฉ2020 Pearson Education, Inc.
Displaying Descriptive Statistics 2-41
Copyright ยฉ2020 Pearson Education, Inc.
2-42 Chapter 2
2.72 A line chart would be the best display for these data.
Note: the data set runs from 1959 to 2017, not 1970 to 2017
Copyright ยฉ2020 Pearson Education, Inc.
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