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University of North Carolina, Greensboro
ECO 25
CHAPTER 2: DESCRIPTIVE STATISTICS: TABULAR AND GRAPHICAL PRESENTATIONS
MULTIPLE CHOICE
1)The minimum number of variables represented in a bar chart is
1
2
3
4
The minimum number of variables represented in a histogram is
1
2
3
4
Which of the following graphical methods is most appropriate for categorical data?
ogive
pie chart
histogram
scatter diagram
In a stemandleaf display,
a single digit is used to define each stem, and a single digit is used to define each leaf
a single digit is used to define each stem, and one or more digits are used to define each leaf
one or more digits are used to define each stem, and a single digit is used to define each leaf
one or more digits are used to define each stem, and one or more digits are used to define each leaf
A graphical method that can be used to show both the rank order and shape of a data set simultaneously is a
relative frequency distribution
pie chart
stemandleaf display
pivot table
The proper way to construct a stemandleaf display for the data set {62, 67, 68, 73, 73, 79, 91, 94, 95, 97} is to
exclude a stem labeled ‘8’
include a stem labeled ‘8’ and enter no leaves on the stem
include a stem labeled ‘(8)’ and enter no leaves on the stem
include a stem labeled ‘8’ and enter one leaf value of ‘0’ on the stem
Data that provide labels or names for groupings of like items are known as
categorical data
quantitative data
label data
generic data
A researcher is gathering data from four geographical areas designated: South ? 1; North ? 2;
East ? 3; West ? 4
University of North Carolina, Greensboro
ECO 25
CHAPTER 2: DESCRIPTIVE STATISTICS: TABULAR AND GRAPHICAL PRESENTATIONS
MULTIPLE CHOICE
1)The minimum number of variables represented in a bar chart is
1
2
3
4
The minimum number of variables represented in a histogram is
1
2
3
4
Which of the following graphical methods is most appropriate for categorical data?
ogive
pie chart
histogram
scatter diagram
In a stemandleaf display,
a single digit is used to define each stem, and a single digit is used to define each leaf
a single digit is used to define each stem, and one or more digits are used to define each leaf
one or more digits are used to define each stem, and a single digit is used to define each leaf
one or more digits are used to define each stem, and one or more digits are used to define each leaf
A graphical method that can be used to show both the rank order and shape of a data set simultaneously is a
relative frequency distribution
pie chart
stemandleaf display
pivot table
The proper way to construct a stemandleaf display for the data set {62, 67, 68, 73, 73, 79, 91, 94, 95, 97} is to
exclude a stem labeled ‘8’
include a stem labeled ‘8’ and enter no leaves on the stem
include a stem labeled ‘(8)’ and enter no leaves on the stem
include a stem labeled ‘8’ and enter one leaf value of ‘0’ on the stem
Data that provide labels or names for groupings of like items are known as
categorical data
quantitative data
label data
generic data
A researcher is gathering data from four geographical areas designated: South ? 1; North ? 2;
East ? 3; West ? 4
Economics
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University of North Carolina, Greensboro
ECO 25
CHAPTER 2: DESCRIPTIVE STATISTICS: TABULAR AND GRAPHICAL PRESENTATIONS
MULTIPLE CHOICE
1)The minimum number of variables represented in a bar chart is

 1
 2
 3
 4
 The minimum number of variables represented in a histogram is
 1
 2
 3
 4
 Which of the following graphical methods is most appropriate for categorical data?
 ogive
 pie chart
 histogram
 scatter diagram
 In a stemandleaf display,
 a single digit is used to define each stem, and a single digit is used to define each leaf
 a single digit is used to define each stem, and one or more digits are used to define each leaf
 one or more digits are used to define each stem, and a single digit is used to define each leaf
 one or more digits are used to define each stem, and one or more digits are used to define each leaf
 A graphical method that can be used to show both the rank order and shape of a data set simultaneously is a
 relative frequency distribution
 pie chart
 stemandleaf display
 pivot table
 The proper way to construct a stemandleaf display for the data set {62, 67, 68, 73, 73, 79, 91, 94, 95, 97} is to
 exclude a stem labeled ‘8’
 include a stem labeled ‘8’ and enter no leaves on the stem
 include a stem labeled ‘(8)’ and enter no leaves on the stem
 include a stem labeled ‘8’ and enter one leaf value of ‘0’ on the stem
 Data that provide labels or names for groupings of like items are known as
 categorical data
 quantitative data
 label data
 generic data
 A researcher is gathering data from four geographical areas designated: South ? 1; North ? 2;
East ? 3; West ? 4. The designated geographical regions represent

 categorical data
 quantitative data
 directional data
 either quantitative or categorical data
 Data that indicate how much or how many are know as
 categorical data

 quantitative data
 label data
 category data
 The ages of employees at a company represent
 categorical data
 quantitative data
 label data
 time series data
 A frequency distribution is
 a tabular summary of a set of data showing the fraction of items in each of several nonoverlapping classes
 a graphical form of representing data
 a tabular summary of a set of data showing the number of items in each of several nonoverlapping classes
 a graphical device for presenting categorical data
 The sum of frequencies for all classes will always equal
 1
 the number of elements in a data set
 the number of classes
 a value between 0 and 1
 In constructing a frequency distribution, as the number of classes are decreased, the class width
 decreases
 remains unchanged
 increases
 can increase or decrease depending on the data values
 If several frequency distributions are constructed from the same data set, the distribution with the widest class width will have the
 fewest classes
 most classes
 same number of classes as the other distributions since all are constructed from the same data
 None of the other answers are correct.
 Excel's can be used to construct a frequency distribution for categorical data.
 DISTRIBUTION function
 SUM function
 FREQUENCY function
 COUNTIF function
 A tabular summary of a set of data showing the fraction of the total number of items in several nonoverlapping classes is a
 frequency distribution.
 relative frequency distribution.
 frequency.
 cumulative frequency distribution.
 The relative frequency of a class is computed by
 dividing the midpoint of the class by the sample size.
 dividing the frequency of the class by the midpoint.
 dividing the sample size by the frequency of the class.
 dividing the frequency of the class by the sample size.
 The sum of the relative frequencies for all classes will always equal
 the sample size
 the number of classes
 one
d. 100
 A tabular summary of data showing the percentage of items in each of several nonoverlapping classes is a
 frequency distribution
 relative frequency distribution
 percent frequency distribution
 cumulative percent frequency distribution
 The percent frequency of a class is computed by
 multiplying the relative frequency by 10
 dividing the relative frequency by 100
 multiplying the relative frequency by 100
 adding 100 to the relative frequency
 The sum of the percent frequencies for all classes will always equal
 one
 the number of classes
 the number of items in the study
d. 100
 In a cumulative frequency distribution, the last class will always have a cumulative frequency equal to
 one
b. 100%
 the total number of elements in the data set
 None of the other answers are correct.
 In a cumulative relative frequency distribution, the last class will have a cumulative relative frequency equal to
 one
 zero
c. 100
d. None of the other answers are correct.
 In a cumulative percent frequency distribution, the last class will have a cumulative percent frequency equal to
 one
b. 100
 the total number of elements in the data set
 None of the other answers are correct.
 The difference between the lower class limits of adjacent classes provides the
 number of classes
 class limits
 class midpoint
 class width
 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)
 histogram
 stemandleaf display
 ogive
 bar chart
 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
 histogram
 stemandleaf display
 pie chart

 bar chart
 Categorical data can be graphically represented by using a(n)
 histogram
 frequency polygon
 ogive
 bar chart
 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 line graph
 only a bar chart
 only a pie chart
 both a bar chart and a pie chart
 Methods that use simple arithmetic and easytodraw graphs to summarize data quickly are called
 exploratory data analysis
 relative frequency distributions
 bar charts
 pie charts
 The total number of data items with a value less than or equal to the upper limit for the class is given by the
 frequency distribution
 relative frequency distribution
 cumulative frequency distribution
 cumulative relative frequency distribution
 Excel's can be used to construct a frequency distribution for quantitative data.
 COUNTIF function
 SUM function
 PivotTable Report
 AVERAGE function
 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
 histogram
 bar chart
 stemandleaf display
 pie chart
 A common graphical presentation of quantitative data is a
 histogram
 bar chart
 relative frequency
 pie chart
 When using Excel to create a one must edit the chart to remove the gaps between rectangles.
 scatter diagram
 bar chart
 histogram
 pie chart
 A can be used to graphically present quantitative data.
 histogram
 pie chart
 stemandleaf display

 both a histogram and a stemandleaf display are correct
 A(n) is a graph of a cumulative distribution.
 histogram
 pie chart
 stemandleaf display
 ogive
 Excel's Chart Tools can be used to construct a
 bar chart
 pie chart
 histogram
 All of these can be constructed using Excel's Chart Tools.
 To construct a bar chart using Excel's Chart Tools, choose as the chart type.
 column
 pie
 scatter
 line
 To construct a pie chart using Excel's Chart Tools, choose as the chart type.
 column
 pie
 scatter
 line
 To construct a histogram using Excel's Chart Tools, choose as the chart type.
 column
 pie

 scatter
 line
 Excel's Chart Tools does not have a chart type for constructing a
 bar chart
 pie chart
 histogram
 stemandleaf display
 A tabular method that can be used to summarize the data on two variables simultaneously is called
 simultaneous equations
 a crosstabulation
 a histogram
 a dot plot
 Excel's can be used to construct a crosstabulation.
 Chart Tools
 SUM function
 PivotTable Report
 COUNTIF function
 In a crosstabulation
 both variables must be categorical
 both variables must be quantitative
 one variable must be categorical and the other must be quantitative
 either or both variables can be categorical or quantitative
 A graphical presentation of the relationship between two quantitative variables is

 a pie chart
 a histogram
 a crosstabulation
 a scatter diagram
 Excel's can be used to construct a scatter diagram.
 Chart Tools
 SUM function
 CROSSTAB function
 RAND function
 When the conclusions based upon the aggregated crosstabulation can be completely reversed if we look at the unaggregated data, the occurrence is known as
 reverse correlation
 inferential statistics
 Simpson's paradox
 disaggregation
 Before drawing any conclusions about the relationship between two variables shown in a crosstabulation, you should
 investigate whether any hidden variables could affect the conclusions
 construct a scatter diagram and find the trendline
 develop a relative frequency distribution
 construct an ogive for each of the variables
 A histogram is not appropriate for displaying which of the following types of information?

 frequency
 relative frequency
 cumulative frequency
 percent frequency
 For stemandleaf displays where the leaf unit is not stated, the leaf unit is assumed to equal
 0
 .1
 1
 10
 Which of the following graphical methods is not intended for quantitative data?
 ogive
 dot plot
 scatter diagram
 pie chart
 Which of the following is least useful in studying the relationship between two variables?
 trendline
 stemandleaf display
 crosstabulation
 scatter diagram
 The sum of the relative frequencies in any relative frequency distribution always equals
 the number of observations
b. 1.00
c. 100
d. the number of variables
 The sum of the frequencies in any frequency distribution always equals
 the number of observations
b. 1.00
c. 100
d. the number of variables
Exhibit 21
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

 Refer to Exhibit 21. The class width for this distribution
 is 9
 is 10
 is 39, which is: the largest value minus the smallest value or 39 ? 0 ? 39
 varies from class to class
 Refer to Exhibit 21. The midpoint of the last class is
 50
 34
 35
d. 34.5
 Refer to Exhibit 21. The number of students working 19 hours or less
 is 80
 is 100
 is 180
 is 300
 Refer to Exhibit 21. The relative frequency of students working 9 hours or less
 is 20
 is 100

c. is 0.95
d. 0.05


60.

Refer to Exhibit 21.
 is 300
 is 0.25
 is 0.75
 is 0.5

The cumulative relative frequency for the class of 20 ? 29




61.

Refer to Exhibit 21. a. 20%
b. 25%
c. 75%
d. 80%

The percentage of students working 10 ? 19 hours is




62.

Refer to Exhibit 21. a. 20%
b. 25%
c. 75%
d. 80%

The percentage of students working 19 hours or less is




63.

Refer to Exhibit 21. a. 100%
b. 75%
c. 50%
d. 25%

The cumulative percent frequency for the class of 30 ? 39 is




64.

Refer to Exhibit 21.
a. is 200

The cumulative frequency for the class of 20 ? 29

 is 300
 is 0.75
 is 0.50
 Refer to Exhibit 21. 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
 Refer to Exhibit 21. The percentage of students who work at least 10 hours per week is a. 50%
b. 5%
c. 95%
d. 100%
Exhibit 22
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

 Refer to Exhibit 22. The number of industries that are classified as retail is
 32
 18
c. 0.36
d. 36%
 Refer to Exhibit 22. The relative frequency of industries that are classified as banking is
 7
b. 0.07
c. 0.70
d. 0.14
 Refer to Exhibit 22. The percent frequency of industries that are classified as electronics is
 10
 20
c. 0.10
d. 0.20
Exhibit 23
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

 Refer to Exhibit 23. The class width for this distribution
 is 5
 is 6
 is 20, which is: the largest value minus the smallest value or 20 ? 0 ? 20
 varies from class to class
 Refer to Exhibit 23. The midpoint of the first class is
 10
 2
c. 2.5
d. 3
 Refer to Exhibit 23. The number of workers who took less than 11 sick days per month
 was 15
 was 200
 was 185
 was 65
 Refer to Exhibit 23. The number of workers who took at most 10 sick days per month
 was 15
 was 200
 was 185
 was 65
 Refer to Exhibit 23. The number of workers who took more than 10 sick days per month
 was 15
 was 200
 was 185
 was 65
 Refer to Exhibit 23. The number of workers who took at least 11 sick days per month
 was 15
 was 200
 was 185
 was 65
 Refer to Exhibit 23. The relative frequency of workers who took 10 or fewer sick days
 was 185
 was 0.925
 was 93
 was 15
 Refer to Exhibit 23. The cumulative relative frequency for the class of 11 ? 15
 is 199
 is 0.07
 is 1
d. is 0.995
 Refer to Exhibit 23. The percentage of workers who took 0  5 sick days per month was a. 20%
b. 120%
c. 75%
d. 60%
 Refer to Exhibit 23. The cumulative percent frequency for the class of 16 ? 20 is a. 100%
b. 65%
c. 92.5%
d. 0.5%
 Refer to Exhibit 23. The cumulative frequency for the class of 11 ? 15
 is 200
 is 14
 is 199
 is 1
Exhibit 24
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

 Refer to Exhibit 24. What percentage of the students does not plan to go to graduate school? a. 280
b. 520
 65
 32
 Refer to Exhibit 24. What percentage of the students' undergraduate major is engineering? a. 292
b. 520
c. 65
d. 36.5
 Refer to Exhibit 24. 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
 Refer to Exhibit 24. Among the students who plan to go to graduate school, what percentage indicated "Other" majors?
a. 15.75
 45
 54
 35