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10. 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
11. 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?
Hours/Day
Frequency
0 − 1
10
1 − 3
45
3 − 5
20
5 − 7
20
7 − 9
5
12. 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
13. 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.
14. 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
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.
15. 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.
16. 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
17. 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
18. 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
19. 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
20. 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
21. 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
22. 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.
23. 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 less than 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?
24. 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?
25. 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
26. 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
64
45
63
40
68
39
65
38
67
42
66
45
65
43
64
35
66
33
27. 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
28. What type of graph is depicted below?
29. What type of relationship is depicted in the following scatter diagram?
30. What type of relationship is depicted in the following scatter diagram?
31. What type of relationship is depicted in the following scatter diagram?
32. 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
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.
33. 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 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.
34. 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
35. 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.
36. 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.
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?
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
37. 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.
Price
Style
Price
Style
Price
Style
<99
Colonial
>100
A-Frame
>100
Colonial
<99
Ranch
>100
Split-Level
<99
Colonial
>100
Split-Level
<99
Colonial
<99
A-Frame
>100
Split-Level
>100
Ranch
>100
Split-Level
<99
Colonial
>100
Colonial
>100
Ranch
<99
A-Frame
<99
A-Frame
<99
Split-Level
<99
Split-Level
<99
Split-Level
>100
Split-Level
<99
A-Frame
<99
Split-Level
>100
Colonial
>100
Ranch
<99
Colonial
>100
Ranch
>100
Split-Level
<99
Ranch
>100
Split-Level
<99
A-Frame
>100
Split-Level
<99
Colonial
<99
Colonial
>100
Colonial
>100
Colonial
>100
Ranch
<99
Split-Level
<99
Split-Level
<99
Colonial
Prepare a crosstabulation for the variables price and style.
38. 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 seg-
ment 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 news-
paper and collected the data listed below.
Segment
of City
Selling
Price
($000)
House Size
(00 sq. ft.)
Number of
Bedrooms
Number of
Bathrooms
Garage
Size
(cars)
Northwest 290 21 4 2 2
South 95 11 2 1 0
Northeast 170 19 3 2 2
Northwest 375 38 5 4 3
West 350 24 4 3 2
South 125 10 2 2 0
West 310 31 4 4 2
West 275 25 3 2 2
Northwest 340 27 5 3 3
Northeast 215 22 4 3 2
Northwest 295 20 4 3 2
South 190 24 4 3 2
Northwest 385 36 5 4 3
West 430 32 5 4 2
South 185 14 3 2 1
South 175 18 4 2 2
Northeast 190 19 4 2 2
Northwest 330 29 4 4 3
West 405 33 5 4 3
Northeast 170 23 4 2 2
West 365 34 5 4 3
Northwest 280 25 4 2 2
South 135 17 3 1 1
Northeast 205 21 4 3 2
West 260 26 4 3 2
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).
c. Comment on any apparent relationship between the variables.
