# Chapter 02 There are 800 students in the School of Business Administration

Document Type

Test Prep

Book Title

Essentials of Modern Business Statistics 4th (Fourth) Edition By Williams 4th Edition

Authors

J.K

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a. Construct a frequency distribution and graphically represent the

frequency distribution.

b. Construct a relative frequency distribution and graphically represent the

relative frequency distribution.

6. 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.

7. 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 histogram.

b. Construct a cumulative frequency distribution.

c. Construct a relative frequency distribution.

d. Construct a cumulative relative frequency distribution.

8. 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

9. 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

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.

EMBS4 TB02 - 22

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 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?

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?

0

2

4

6

8

10

12

20 30 40 50

x

y

29. What type of relationship is depicted in the following scatter diagram?

0

2

4

6

8

10

12

20 30 40 50

x

y

30. What type of relationship is depicted in the following scatter diagram?

0

2

4

6

8

10

12

20 30 40 50

x

y

31. What type of relationship is depicted in the following scatter diagram?

0

2

4

6

8

10

12

20 30 40 50

x

y

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. One of the decisions Roger must make is how many Mustangs of

each color he should order. The new color options are very similar to the past

year’s options.

Roger believes that the colors chosen by customers who special-order their cars

best reflect most customers’ true color preferences. For that reason, 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 graph showing the frequency distribution of the car colors.

c. Construct a pie chart showing the percent frequency distribution of the car

colors.

Car Color Percent Frequencies

White

17.5%

Green

10.0%

Black

30.0%

Red

25.0%

Blue

17.5%

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

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