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CHAPTER TWO

DESCRIPTIVE STATISTICS:

TABULAR AND GRAPHICAL PRESENTATIONS

MULTIPLE CHOICE QUESTIONS

In the following multiple-choice questions, circle the correct answer.

1. The minimum number of variables represented in a bar graph is

a. one

b. two

c. three

d. four

2. The minimum number of variables represented in a histogram is

a. one

b. two

c. three

d. four

3. Which of the following graphical methods is most appropriate for qualitative

data?

a. ogive

b. pie chart

c. histogram

d. scatter diagram

4. In a stem-and-leaf display,

a. a single digit is used to define each stem, and a single digit is used to

define each leaf

b. a single digit is used to define each stem, and one or more digits are used

to define each leaf

c. one or more digits are used to define each stem, and a single digit is used

to define each leaf

d. one or more digits are used to define each stem, and one or more digits

are used to define each leaf

5. A graphical method that can be used to show both the rank order and shape of a

data set simultaneously is a

a. relative frequency distribution

b. pie chart

c. stem-and-leaf display

d. pivot table

6. The proper way to construct a stem-and-leaf display for the data set {62, 67, 68,

73, 73, 79, 91, 94, 95, 97} is to

a. exclude a stem labeled ‘8’

b. include a stem labeled ‘8’ and enter no leaves on the stem

c. include a stem labeled ‘(8)’ and enter no leaves on the stem

d. include a stem labeled ‘8’ and enter one leaf value of ‘0’ on the stem

7. Data that provide labels or names for categories of like items are known as

a. categorical data

b. quantitative data

c. label data

d. indicator data

8. A researcher is gathering data from four geographical areas designated: South =

1; North = 2; East = 3; West = 4. The designated geographical regions represent

a. categorical data

b. quantitative data

c. label data

d. either categorical or quantitative data

9. Data that indicate how much or how many are know as

a. categorical data

b. quantitative data

c. label data

d. counter data

10. The ages of employees at a company represent

a. categorical data

b. quantitative data

c. label data

d. longevity data

11. A frequency distribution is

a. a tabular summary of a set of data showing the fraction of items in each

of several nonoverlapping classes

b. a graphical form of representing data

c. a tabular summary of a set of data showing the number of items in each

of several nonoverlapping classes

d. a graphical device for presenting categorical data

12. The sum of frequencies for all classes will always equal

a. 1

b. the number of elements in the data set

c. the number of classes

d. a value between 0 and 1

13. In constructing a frequency distribution, as the number of classes are decreased,

the class width

a. decreases

b. remains unchanged

c. increases

d. can increase or decrease depending on the data values

14. If several frequency distributions are constructed from the same data set, the

distribution with the widest class width will have the

a. fewest classes

b. most classes

c. same number of classes as the other distributions since all are

constructed from the same data

d. None of the other answers are correct.

15. Excel’s __________ can be used to construct a frequency distribution for

categorical data.

a. DISTRIBUTION function

b. SUM function

c. FREQUENCY function

d. COUNTIF function

16. A tabular summary of a set of data showing the fraction of the total number of

items in several nonoverlapping classes is a

a. frequency distribution.

b. relative frequency distribution.

c. frequency.

d. cumulative frequency distribution.

17. The relative frequency of a class is computed by

a. dividing the midpoint of the class by the sample size.

b. dividing the frequency of the class by the midpoint.

c. dividing the sample size by the frequency of the class.

d. dividing the frequency of the class by the sample size.

18. The sum of the relative frequencies for all classes will always equal

a. the sample size

b. the number of classes

c. one

d. 100

19. A tabular summary of data showing the percentage of items in each of several

nonoverlapping classes is a

a. frequency distribution

b. relative frequency distribution

c. percent frequency distribution

d. cumulative percent frequency distribution

20. The percent frequency of a class is computed by

a. multiplying the relative frequency by 10

b. dividing the relative frequency by 100

c. multiplying the relative frequency by 100

d. adding 100 to the relative frequency

21. The sum of the percent frequencies for all classes will always equal

a. one

b. the number of classes

c. the number of items in the study

d. 100

22. In a cumulative frequency distribution, the last class will always have a

cumulative frequency equal to

a. one

b. 100%

c. the total number of elements in the data set

d. None of the other answers are correct.

23. In a cumulative relative frequency distribution, the last class will have a

cumulative relative frequency equal to

a. one

b. zero

c. 100

d. None of the other answers are correct.

24. In a cumulative percent frequency distribution, the last class will have a

cumulative percent frequency equal to

a. one

b. 100

c. the total number of elements in the data set

d. None of the other answers are correct.

25. The difference between the lower class limits of adjacent classes provides the

a. number of classes

b. class limits

c. class midpoint

d. class width

Exhibit 2-1

The numbers of hours worked (per week) by 400 statistics students are shown below.

Number of hours

Frequency

0 − 9

20

10 − 19

80

20 − 29

200

30 − 39

100

26. Refer to Exhibit 2-1. The class width for this distribution

a. is 9

b. is 10

c. is 39, which is: the largest value minus the smallest value or 39 − 0 = 39

d. varies from class to class

27. Refer to Exhibit 2-1. The midpoint of the last class is

a. 50

b. 34

c. 35

d. 34.5

28. Refer to Exhibit 2-1. The number of students working 19 hours or less

a. is 80

b. is 100

c. is 180

d. is 300

29. Refer to Exhibit 2-1. The relative frequency of students working 9 hours or less

a. is 20

b. is 100

c. is 0.95

d. 0.05

30. Refer to Exhibit 2-1. The cumulative relative frequency for the class of 20 − 29

a. is 300

b. is 0.25

c. is 0.75

d. is 0.5

31. Refer to Exhibit 2-1. The percentage of students working 10 − 19 hours is

a. 20%

b. 25%

c. 75%

d. 80%

32. Refer to Exhibit 2-1. The percentage of students working 19 hours or less is

a. 20%

b. 25%

c. 75%

d. 80%

33. Refer to Exhibit 2-1. The cumulative percent frequency for the class of 30 − 39

is

a. 100%

b. 75%

c. 50%

d. 25%

34. Refer to Exhibit 2-1. The cumulative frequency for the class of 20 − 29

a. is 200

b. is 300

c. is 0.75

d. is 0.50

35. Refer to Exhibit 2-1. If a cumulative frequency distribution is developed for the

above data, the last class will have a cumulative frequency of

a. 100

b. 1

c. 30 – 39

d. 400

36. Refer to Exhibit 2-1. The percentage of students who work at least 10 hours per

week is

a. 50%

b. 5%

c. 95%

d. 100%

Exhibit 2-2

Information on the type of industry is provided for a sample of 50 Fortune 500

companies.

Industry Type

Frequency

Banking

7

Consumer Products

15

Electronics

10

Retail

18

37. Refer to Exhibit 2-2. The number of industries that are classified as retail is

a. 32

b. 18

c. 0.36

d. 36%

38. Refer to Exhibit 2-2. The relative frequency of industries that are classified as

banking is

a. 7

b. 0.07

c. 0.70

d. 0.14

39. Refer to Exhibit 2-2. The percent frequency of industries that are classified as

electronics is

a. 10

b. 20

c. 0.10

d. 0.20

Exhibit 2-3

The number of sick days taken (per month) by 200 factory workers is summarized below.

Number of Days

Frequency

0 − 5

120

6 − 10

65

11 − 15

14

16 − 20

1

40. Refer to Exhibit 2-3. The class width for this distribution

a. is 5

b. is 6

c. is 20, which is: the largest value minus the smallest value or 20 − 0 = 20

d. varies from class to class

41. Refer to Exhibit 2-3. The midpoint of the first class is

a. 10

b. 2

c. 2.5

d. 3

42. Refer to Exhibit 2-3. The number of workers who took less than 11 sick days per

month

a. was 15

b. was 200

c. was 185

d. was 65

43. Refer to Exhibit 2-3. The number of workers who took at most 10 sick days per

month

a. was 15

b. was 200

c. was 185

d. was 65

44. Refer to Exhibit 2-3. The number of workers who took more than 10 sick days

per month

a. was 15

b. was 200

c. was 185

d. was 65

45. Refer to Exhibit 2-3. The number of workers who took at least 11 sick days per

month

a. was 15

b. was 200

c. was 185

d. was 65

46. Refer to Exhibit 2-3. The relative frequency of workers who took 10 or fewer

sick days

a. was 185

b. was 0.925

c. was 93

d. was 15

47. Refer to Exhibit 2-3. The cumulative relative frequency for the class of 11 − 15

a. is 199

b. is 0.07

c. is 1

d. is 0.995

48. Refer to Exhibit 2-3. The percentage of workers who took 0 – 5 sick days per

month was

a. 20%

b. 120%

c. 75%

d. 60%

49. Refer to Exhibit 2-3. The cumulative percent frequency for the class of 16 − 20

is

a. 100%

b. 65%

c. 92.5%

d. 0.5%

50. Refer to Exhibit 2-3. The cumulative frequency for the class of 11 − 15

a. is 200

b. is 14

c. is 199

d. is 1

51. A graphical device for depicting categorical data that have been summarized in a

frequency distribution, relative frequency distribution, or percent frequency

distribution is a(n)

a. histogram

b. stem-and-leaf display

c. ogive

d. bar graph

52. A graphical device for presenting categorical data summaries based on

subdivision of a circle into sectors that correspond to the relative frequency for

each class is a

a. histogram

b. stem-and-leaf display

c. pie chart

d. bar graph

53. Categorical data can be graphically represented by using a(n)

a. histogram

b. frequency polygon

c. ogive

d. bar graph

54. Fifteen percent of the students in a School of Business Administration are

majoring in Economics, 20% in Finance, 35% in Management, and 30% in

Accounting. The graphical device(s) that can be used to present these data is

(are)

a. a line graph

b. only a bar graph

c. only a pie chart

d. both a bar graph and a pie chart

55. Methods that use simple arithmetic and easy-to-draw graphs to summarize data

quickly are called

a. exploratory data analysis

b. relative frequency distributions

c. bar graphs

d. pie charts

56. The total number of data items with a value less than or equal to the upper limit

for the class is given by the

a. frequency distribution

b. relative frequency distribution

c. cumulative frequency distribution

d. cumulative relative frequency distribution

57. Excel’s __________ can be used to construct a frequency distribution for

quantitative data.

a. COUNTIF function

b. SUM function

c. PivotTable Report

d. AVERAGE function

58. A graphical presentation of a frequency distribution, relative frequency

distribution, or percent frequency distribution of quantitative data constructed by

placing the class intervals on the horizontal axis and the frequencies on the

vertical axis is a

a. histogram

b. bar graph

c. stem-and-leaf display

d. pie chart

59. A common graphical presentation of quantitative data is a

a. histogram

b. bar graph

c. relative frequency

d. pie chart

60. When using Excel to create a __________ one must edit the chart to remove the

gaps between rectangles.

a. scatter diagram

b. bar graph

c. histogram

d. pie chart

61. A __________ can be used to graphically present quantitative data.

a. histogram

b. pie chart

c. stem-and-leaf display

d. both a histogram and a stem-and-leaf display are correct

62. A(n) __________ is a graph of a cumulative distribution.

a. histogram

b. pie chart

c. stem-and-leaf display

d. ogive

63. Excel’s Chart Tools can be used to construct a

a. bar graph

b. pie chart

c. histogram

d. All of these can be constructed using Excel’s Chart Tools.

64. To construct a bar graph using Excel’s Chart Tools, choose __________ as the

chart type.

a. column

b. pie

c. scatter

d. line

65. To construct a pie chart using Excel’s Chart Tools, choose __________ as the

chart type.

a. column

b. pie

c. scatter

d. line

66. To construct a histogram using Excel’s Chart Tools, choose __________ as the

chart type.

a. column

b. pie

c. scatter

d. line

67. Excel’s Chart Tools does not have a chart type for constructing a

a. bar graph

b. pie chart

c. histogram

d. stem-and-leaf display

68. A tabular method that can be used to summarize the data on two variables

simultaneously is called

a. simultaneous equations

b. a crosstabulation

c. a histogram

d. a dot plot

69. Excel’s __________ can be used to construct a crosstabulation.

a. Chart Tools

b. SUM function

c. PivotTable Report

d. COUNTIF function

70. In a crosstabulation

a. both variables must be categorical

b. both variables must be quantitative

c. one variable must be categorical and the other must be quantitative

d. either or both variables can be categorical or quantitative

Exhibit 2-4

A survey of 400 college seniors resulted in the following crosstabulation regarding their

undergraduate major and whether or not they plan to go to graduate school.

Undergraduate Major

Graduate School

Business

Engineering

Others

Total

Yes

35

42

63

140

No

91

104

65

260

Total

126

146

128

400

71. Refer to Exhibit 2-4. What percentage of the students does not plan to go to

graduate school?

a. 280

b. 520

c. 65

d. 32

72. Refer to Exhibit 2-4. What percentage of the students' undergraduate major is

engineering?

a. 292

b. 520

c. 65

d. 36.5

73. Refer to Exhibit 2-4. Of those students who are majoring in business, what

percentage plans to go to graduate school?

a. 27.78

b. 8.75

c. 70

d. 72.22

74. Refer to Exhibit 2-4. Among the students who plan to go to graduate school,

what percentage indicated "Other" majors?

a. 15.75

b. 45

c. 54

d. 35

75. A graphical presentation of the relationship between two quantitative variables is

a. a pie chart

b. a histogram

c. a crosstabulation

d. a scatter diagram

76. Excel’s __________ can be used to construct a scatter diagram.

a. Chart Tools

b. SUM function

c. CROSSTAB function

d. COUNTIF function

77. When the conclusions based upon the aggregated crosstabulation can be

completely reversed if we look at the unaggregated data, the occurrence is known

as

a. reverse correlation

b. inferential statistics

c. Simpson’s paradox

d. disaggregation

78. Before drawing any conclusions about the relationship between two variables

shown in a crosstabulation, you should

a. investigate whether any hidden variables could affect the conclusions

b. construct a scatter diagram and find the trendline

c. develop a relative frequency distribution

d. construct an ogive for each of the variables

PROBLEMS

1. Thirty students in the School of Business were asked what their majors were.

The following represents their responses (M = Management; A = Accounting; E

= Economics; O = Others).

A

M

M

A

M

M

E

M

O

A

E

E

M

A

O

E

M

A

M

A

M

A

O

A

M

E

E

M

A

M

a. Construct a frequency distribution and a bar graph.

b. Construct a relative frequency distribution and a pie chart.

a. and b.

Major

Frequency

Relative Frequency

M

12

0.4

A

9

0.3

E

6

0.2

O

3

0.1

Total

30

1.0

2. Twenty employees of ABC Corporation were asked if they liked or disliked the

new district manager. Below are their responses. Let L represent liked and D

represent disliked.

L

L

D

L

D

D

D

L

L

D

D

L

D

D

L

D

D

D

D

L

a. Construct a frequency distribution and a bar graph.

b. Construct a relative frequency distribution and a pie chart.

3. A student has completed 20 courses in the School of Arts and Sciences. Her

grades in the 20 courses are shown below.

A

B

A

B

C

C

C

B

B

B

B

A

B

B

B

C

B

C

B

A

a. Develop a frequency distribution and a bar graph for her grades.

b. Develop a relative frequency distribution for her grades and construct a

pie chart.

4. A sample of 50 TV viewers were asked, “Should TV sponsors pull their

sponsorship from programs that draw numerous viewer complaints?" Below are

the results of the survey. (Y = Yes; N = No; W = Without Opinion)

N

W

N

N

Y

N

N

N

Y

N

N

Y

N

N

N

N

N

Y

N

N

Y

N

Y

W

N

Y

W

W

N

Y

W

W

N

W

Y

W

N

W

Y

W

N

Y

N

Y

N

W

Y

Y

N

Y

a. Construct a frequency distribution and a bar graph.

b. Construct a relative frequency distribution and a pie chart.

5. 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

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