Chapter 2 – Descriptive Statistics: Tabular and Graphical Displays
93. Forty shoppers were asked if they preferred the weight of a can of soup to be 6 ounces, 8 ounces, or 10 ounces. Below
are their responses.
6
6
6
10
8
8
8
10
6
6
10
10
8
8
6
6
6
8
6
6
8
8
8
10
8
8
6
10
8
6
6
8
8
8
10
10
8
10
8
6
a.
Construct a frequency distribution and graphically represent the frequency distribution.
b.
Construct a relative frequency distribution and graphically represent the relative frequency
distribution.
a. and b.
Preferences
Frequency
Relative Frequency
6 ounces
14
0.350
8 ounces
17
0.425
10 ounces
9
0.225
Total
40
1.000
1
94. There are 800 students in the School of Business Administration. There are four majors in the School: Accounting,
Finance, Management, and Marketing. The following shows the number of students in each major.
Major
Number of Students
Accounting
240
Finance
160
Management
320
Marketing
80
Develop a percent frequency distribution and construct a bar chart and a pie chart.
Major
Percent Frequency
Accounting
30%
Finance
20%
Management
40%
Marketing
10%
1
95. Below you are given the examination scores of 20 students.
52
99
92
86
84
63
72
76
95
88
92
58
65
79
80
90
75
74
56
99
a.
Construct a frequency distribution for this data. Let the first class be 50 – 59 and draw a
Response
Frequency
Relative Frequency
24
0.48
15
0.30
Without Opinion
11
0.22
Total
50
1.00
Chapter 2 – Descriptive Statistics: Tabular and Graphical Displays
histogram.
b.
Construct a cumulative frequency distribution.
c.
Construct a relative frequency distribution.
d.
Construct a cumulative relative frequency distribution.
a.
b.
c.
d.
Relative
Cumulative
Cumulative
Score
Frequency
Frequency
Frequency
Relative Frequency
50 − 59
3
3
0.15
0.15
60 − 69
2
5
0.10
0.25
70 − 79
5
10
0.25
0.50
80 − 89
4
14
0.20
0.70
90 − 99
6
20
0.30
1.00
Total
20
1.00
96. Two hundred members of a fitness center were surveyed. One survey item stated, “The facilities are always clean.”
The members’ responses to the item are summarized below. Fill in the missing value for the frequency distribution.
Opinion
Frequency
Strongly Agree
63
Agree
92
Disagree
Strongly Disagree
15
No Opinion
14
16
97. Fill in the missing value for the following relative frequency distribution.
Opinion
Relative Frequency
Strongly Agree
0.315
Agree
0.460
Disagree
Strongly Disagree
0.075
No Opinion
0.070
0.080
98. Fill in the missing value for the following percent frequency distribution.
Annual Salaries
Percent Frequency
Under $30,000
10
$30,000 − 49,999
35
$50,000 − 69,999
40
$70,000 − 89,999
$90,000 and over
5
10
99. The following is a summary of the number of hours spent per day watching television for a sample of 100 people.
What is wrong with the frequency distribution?
Chapter 2 – Descriptive Statistics: Tabular and Graphical Displays
Hours/Day
Frequency
0 − 1
10
1 − 3
45
3 − 5
20
5 − 7
20
7 − 9
5
ANSWER:
The classes overlap.
POINTS:
1
100. A summary of the results of a job satisfaction survey follows. What is wrong with the relative frequency distribution?
Rating
Relative Frequency
Poor
.15
Fair
.45
Good
.25
Excellent
.30
ANSWER:
The relative frequencies do not sum to 1.
POINTS:
1
101. The frequency distribution below was constructed from data collected from a group of 25 students.
Height in Inches
Frequency
58 − 63
3
64 − 69
5
70 − 75
2
76 − 81
6
82 − 87
4
88 − 93
3
94 − 99
2
a.
Construct a relative frequency distribution.
b.
Construct a cumulative frequency distribution.
c.
Construct a cumulative relative frequency distribution.
a.
b.
c.
Relative
Cumulative
Cumulative
Height (inches)
Frequency
Frequency
Frequency
Relative Frequency
58 − 63
3
0.12
3
0.12
64 − 69
5
0.20
8
0.32
70 − 75
2
0.08
10
0.40
76 − 81
6
0.24
16
0.64
82 − 87
4
0.16
20
0.80
88 − 93
3
0.12
23
0.92
94 − 99
2
0.08
25
1.00
1.00
POINTS:
1
102. The frequency distribution below was constructed from data collected on the quarts of soft drinks consumed per
week by 20 students.
Quarts of Soft Drink
Frequency
0 − 3
4
Chapter 2 – Descriptive Statistics: Tabular and Graphical Displays
4 − 7
5
8 − 11
6
12 − 15
3
16 − 19
2
a.
Construct a relative frequency distribution.
b.
Construct a cumulative frequency distribution.
c.
Construct a cumulative relative frequency distribution.
a.
b.
c.
Quarts of Soft Drinks
Relative Frequency
0 − 3
4 − 7
8 − 11
15
12 − 15
18
16 − 19
20
1
103. The grades of 10 students on their first management test are shown below.
94
61
96
66
92
68
75
85
84
78
a.
Construct a frequency distribution. Let the first class be 60 − 69.
b.
Construct a cumulative frequency distribution.
c.
Construct a relative frequency distribution.
a.
b.
c.
60 − 69
70 − 79
80 − 89
90 − 99
10
10
1
104. You are given the following data on the ages of employees at a company. Construct a stem-and-leaf display. Specify
the leaf unit for the display.
26
32
28
45
58
52
44
36
42
27
41
53
55
48
32
42
44
40
36
37
2 | 6
7
8
3 | 2
2
6
6
7
4 | 0
1
2
4
4
5
8
5 | 2
3
5
8
1
105. Construct a stem-and-leaf display for the following data. Specify the leaf unit for the display.
12
52
51
37
47
40
38
26
57
31
49
43
45
19
36
32
44
48
22
18
8
9
6
2
6
7
8
3
4
5
7
8
9
2
7
1
106. You are given the following data on the earnings per share for ten companies. Construct a stem-and-leaf display.
Specify the leaf unit for the display.
2.6
1.4
1.3
0.5
2.2
1.1
1.1
0.7
0.9
2.0
7
9
1
3
4
2
6
1
107. You are given the following data on the annual salaries for eight employees. Construct a stem-and-leaf display.
Specify the leaf unit for the display.
$26,500
$27,850
$25,000
$27,460
$26,890
$25,400
$26,150
$30,000
25 | 0
4
26 | 1
5
8
27 | 4
8
28 |
29 |
30 | 0
1
108. You are given the following data on the price/earnings (P/E) ratios for twelve companies. Construct a stem-and-leaf
display. Specify the leaf unit for the display.
23
25
39
47
22
37
8
36
48
28
37
26
3
5
6
8
8
1
109. You are given the following data on times (in minutes) to complete a race. Construct a stem-and-leaf display. Specify
the leaf unit for the display.
15.2
15.8
12.4
11.9
15.2
14.7
14.8
11.8
12.0
12.1
Leaf Unit = 0.1
11 | 8
12 | 0
13 |
14 | 7
15 | 2
110. The SAT math scores of a sample of business school students and their genders are shown below.
SAT Math Scores
Gender
Less than 400
400 up to 600
600 and more
Total
Female
24
168
48
240
Male
40
96
24
160
Total
64
264
72
400
a.
How many students scored less than 400?
b.
How many students were female?
c.
Of the male students, how many scored 600 or more?
d.
Compute row percentages and comment on any relationship that may exist between SAT
math scores and gender of the individuals.
e.
Compute column percentages.
a.
64
b.
240
c.
24
d.
SAT Math Scores
Gender
Less than 400
400 up to 600
600 and more
Total
Female
10%
70%
20%
100%
Male
25%
60%
15%
100%
e.
SAT Math Scores
Gender
Less than 400
400 up to 600
600 and more
Female
37.5%
63.6%
66.7%
Male
62.5%
36.4%
33.3%
Total
100%
100%
100%
111. A market research firm has conducted a study to determine consumer preference for a new package design for a
particular product. The consumers, ages were also noted.
Package Design
Age
A
B
C
Total
Under 25
18
18
29
65
25 – 40
18
12
5
35
Total
36
30
34
100
a.
Which package design was most preferred overall?
b.
What percent of those participating in the study preferred package A?
c.
What percent of those under 25 years of age preferred package A?
d.
What percent of those aged 25 − 40 preferred package A?
e.
Is the preference for package A the same for both age groups?
a.
Design A
b.
36%
c.
27.7%
d.
51.4%
(27.7% vs. 51.4%).
POINTS:
1
112. Partial results of a study follow in a crosstabulation of column percentages.
Method of Payment
Gender
Cash
Credit Card
Check
Female
18%
50%
90%
Male
82%
50%
10%
Total
100%
100%
100%
a.
Interpret the 18% found in the first row and first column of the crosstabulation.
b.
If 50 of those in the study paid by check, how many of the males paid by check?
a.
b.
POINTS:
1
113. For the following observations, plot a scatter diagram and indicate what kind of relationship (if any) exist between x
and y.
x
y
2
7
6
19
3
9
5
17
4
11
ANSWER:
A positive relationship between x and y appears to exist.
POINTS:
1
114. For the following observations, plot a scatter diagram and indicate what kind of relationship (if any) exists between
women’s height (inches) and annual starting salary ($1000).
Height
Salary
Chapter 2 – Descriptive Statistics: Tabular and Graphical Displays
64
45
63
40
68
39
65
38
67
42
66
45
65
43
64
35
66
33
115. For the following observations, plot a scatter diagram and indicate what kind of relationship (if any) exists between
the amount of sugar in one serving of cereal (grams) and the amount of fiber in one serving of cereal (grams).
Sugar
Fiber
1.2
3.2
1.3
3.1
1.5
2.8
1.8
2.4
2.2
1.1
2.8
1.3
3.0
1.0
A negative relationship between amount of sugar and amount of fiber appears to exist.
116. What type of graph is depicted below?
A scatter diagram
117. What type of relationship is depicted in the following scatter diagram?
Chapter 2 – Descriptive Statistics: Tabular and Graphical Displays
118. What type of relationship is depicted in the following scatter diagram?
119. What type of relationship is depicted in the following scatter diagram?
120. It is time for Roger Hall, manager of new car sales at the Maxwell Ford dealership, to submit his order for new
Mustang coupes. These cars will be parked in the lot, available for immediate sale to buyers who are not special-ordering
a car. Roger must decide how many Mustangs of each color he should order. The new color options are very similar to the
past year’s options.
Roger believes the colors chosen by customers who special-order their cars best reflect most customers’ true color
preferences. He has taken a random sample of 40 special orders for Mustang coupes placed in the past year. The color
preferences found in the sample are listed below.
Blue
Black
Green
White
Black
Red
Red
White
Chapter 2 – Descriptive Statistics: Tabular and Graphical Displays
Black
Red
White
Blue
Blue
Green
Red
Black
Red
White
Blue
White
Red
Red
Black
Black
Green
Black
Red
Black
Blue
Black
White
Green
Blue
Red
Black
White
Black
Red
Black
Blue
a. Prepare a frequency distribution, relative frequency distribution, and percent frequency distribution for the data set.
b. Construct a bar chart showing the frequency distribution of the car colors.
c. Construct a pie chart showing the percent frequency distribution of the car colors.
Frequency
Frequency
Frequency
Black
0.300
30.0
Blue
0.175
17.5
Green
0.100
10.0
Red
0.250
25.0
White
0.175
17.5
Total
1.000
100.0
121. Missy Walters owns a mail-order business specializing in clothing, linens, and furniture for children. She is
considering offering her customers a discount on shipping charges for furniture based on the dollar-amount of the
furniture order. Before Missy decides the discount policy, she needs a better understanding of the dollar-amount
Chapter 2 – Descriptive Statistics: Tabular and Graphical Displays
distribution of the furniture orders she receives.
Missy had an assistant randomly select 50 recent orders that included furniture. The assistant recorded the value, to the
nearest dollar, of the furniture portion of each order. The data collected is listed below.
136
281
226
123
178
445
231
389
196
175
211
162
212
241
182
290
434
167
246
338
194
242
368
258
323
196
183
209
198
212
277
348
173
409
264
237
490
222
472
248
231
154
166
214
311
141
159
362
189
260
a. Prepare a frequency distribution, relative frequency distribution, and percent frequency distribution for the data set
using a class width of $50.
b. Construct a histogram showing the percent frequency distribution of the furniture-order values in the sample.
c. Develop a cumulative frequency distribution and a cumulative percent frequency distribution for this data.
100-149
150-199
15
30
200-249
14
28
250-299
12
300-349
350-399
400-449
450-499
100-149
150-199
15
18
36
200-249
14
32
64
250-299
38
76
300-349
42
84
350-399
45
90
400-449
48
96
450-499
50
100
122. Develop a stretched stem-and-leaf display for the data set below, using a leaf unit of 10.
136
281
226
123
178
445
231
389
196
175
211
162
212
241
182
290
434
167
246
338
194
242
368
258
323
196
183
209
198
212
277
348
173
409
264
237
490
222
472
248
231
154
166
214
311
141
159
362
189
260
123. Ithaca Log Homes manufactures four styles of log houses that are sold in kits. The price (in $000) and style of
homes the company has sold in the past year are shown below.
Chapter 2 – Descriptive Statistics: Tabular and Graphical Displays
Prepare a crosstabulation for the variables price (as rows) and style (as columns).
124. Tony Zamora, a real estate investor, has just moved to Clarksville and wants to learn about the local real estate
market. He wants to understand, for example, the relationship between geographical segment of the city and selling price
of a house, the relationship between selling price and number of bedrooms, and so on. Tony has randomly selected 25
house-for-sale listings from the Sunday newspaper and collected the data listed below.
Chapter 2 – Descriptive Statistics: Tabular and Graphical Displays
a) Construct a crosstabulation for the variables segment of city and number of bedrooms.
b) Compute the row percentages for your crosstabulation in part (a).
Chapter 2 – Descriptive Statistics: Tabular and Graphical Displays
125. The manager of Hudson Auto Repair would like to get a better picture of the distribution of costs for new parts used
in the engine tune-up jobs done in the garage. A sample of 50 customer invoices for tune-ups has been taken and the costs
of parts, rounded to the nearest dollar, are listed below.
91
78
93
57
75
52
99
80
73
62
71
69
72
89
66
75
79
75
72
76
104
74
62
68
97
105
77
65
80
109
85
97
88
68
83
68
71
69
67
74
62
82
98
101
79
105
79
69
62
73
Develop a frequency distribution for these cost data. Use your own judgment to determine the number of classes and
class width that provide a distribution that will be meaningful and helpful to the manager.
a. Develop a stem-and-leaf display showing both the rank order and shape of the data set.
b. Develop a stretched stem-and-leaf display using two stems for each leading digit(s).
c. Which display is better at revealing the natural grouping and variation in the data?
POINTS:
1
126. Guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent, above
average, average, below average, or poor. The ratings provided by a sample of 20 quests are shown below.
Below Average Average Above Average Above Average
Above Average Above Average Above Average Below Average
Below Average Average Poor Poor
Above Average Average Above Average Average
Excellent Above Average Average Above Average
a. Provide a frequency distribution showing the number of occurrences of each rating level in the sample.
b. Construct relative frequency and percent frequency distributions for the data.
c. Display the frequencies graphically with a bar graph.
d. Display the percent frequencies graphically with a pie chart.
