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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 stem-and-leaf 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 stem-and-leaf display pivot table                                                  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 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

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. 1
2. 2
3. 3
4. 4

1. The minimum number of variables represented in a histogram is
1. 1
2. 2
3. 3
4. 4

1. Which of the following graphical methods is most appropriate for categorical data?
1. ogive
2. pie chart
3. histogram
4. scatter diagram

1. In a stem-and-leaf display,
1. a single digit is used to define each stem, and a single digit is used to define each leaf
2. a single digit is used to define each stem, and one or more digits are used to define each leaf
3. one or more digits are used to define each stem, and a single digit is used to define each leaf
4. one or more digits are used to define each stem, and one or more digits are used to define each leaf

1. A graphical method that can be used to show both the rank order and shape of a data set simultaneously is a
1. relative frequency distribution
2. pie chart
3. stem-and-leaf display
4. pivot table

1. 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
1. exclude a stem labeled ‘8’
2. include a stem labeled ‘8’ and enter no leaves on the stem
3. include a stem labeled ‘(8)’ and enter no leaves on the stem
4. include a stem labeled ‘8’ and enter one leaf value of ‘0’ on the stem

1. Data that provide labels or names for groupings of like items are known as
1. categorical data
2. quantitative data
3. label data
4. generic data

1. A researcher is gathering data from four geographical areas designated: South ? 1; North ? 2;

East ? 3; West ? 4. The designated geographical regions represent

1. categorical data
2. quantitative data
3. directional data
4. either quantitative or categorical data

1. Data that indicate how much or how many are know as
1. categorical data

1. quantitative data
2. label data
3. category data

1. The ages of employees at a company represent
1. categorical data
2. quantitative data
3. label data
4. time series data

1. A frequency distribution is
1. a tabular summary of a set of data showing the fraction of items in each of several nonoverlapping classes
2. a graphical form of representing data
3. a tabular summary of a set of data showing the number of items in each of several nonoverlapping classes
4. a graphical device for presenting categorical data

1. The sum of frequencies for all classes will always equal
1. 1
2. the number of elements in a data set
3. the number of classes
4. a value between 0 and 1

1. In constructing a frequency distribution, as the number of classes are decreased, the class width
1. decreases
2. remains unchanged
3. increases
4. can increase or decrease depending on the data values

1. If several frequency distributions are constructed from the same data set, the distribution with the widest class width will have the
1. fewest classes
2. most classes
3. same number of classes as the other distributions since all are constructed from the same data
4. None of the other answers are correct.

1. Excel's                              can be used to construct a frequency distribution for categorical data.
1. DISTRIBUTION function
2. SUM function
3. FREQUENCY function
4. COUNTIF function

1. A tabular summary of a set of data showing the fraction of the total number of items in several nonoverlapping classes is a
1. frequency distribution.
2. relative frequency distribution.
3. frequency.
4. cumulative frequency distribution.

1. The relative frequency of a class is computed by
1. dividing the midpoint of the class by the sample size.
2. dividing the frequency of the class by the midpoint.
3. dividing the sample size by the frequency of the class.
4. dividing the frequency of the class by the sample size.

1. The sum of the relative frequencies for all classes will always equal
1. the sample size
2. the number of classes
3. one

d. 100

1. A tabular summary of data showing the percentage of items in each of several nonoverlapping classes is a
1. frequency distribution
2. relative frequency distribution
3. percent frequency distribution
4. cumulative percent frequency distribution

1. The percent frequency of a class is computed by
1. multiplying the relative frequency by 10
2. dividing the relative frequency by 100
3. multiplying the relative frequency by 100
4. adding 100 to the relative frequency

1. The sum of the percent frequencies for all classes will always equal
1. one
2. the number of classes
3. the number of items in the study

d. 100

1. In a cumulative frequency distribution, the last class will always have a cumulative frequency equal to
1. one

b. 100%

1. the total number of elements in the data set
2. None of the other answers are correct.

1. In a cumulative relative frequency distribution, the last class will have a cumulative relative frequency equal to
1. one
2. zero

c. 100

d. None of the other answers are correct.

1. In a cumulative percent frequency distribution, the last class will have a cumulative percent frequency equal to
1. one

b. 100

1. the total number of elements in the data set
2. None of the other answers are correct.

1. The difference between the lower class limits of adjacent classes provides the
1. number of classes
2. class limits
3. class midpoint
4. class width

1. 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)
1. histogram
2. stem-and-leaf display
3. ogive
4. bar chart

1. 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
1. histogram
2. stem-and-leaf display
3. pie chart

1. bar chart

1. Categorical data can be graphically represented by using a(n)
1. histogram
2. frequency polygon
3. ogive
4. bar chart

1. 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)
1. a line graph
2. only a bar chart
3. only a pie chart
4. both a bar chart and a pie chart

1. Methods that use simple arithmetic and easy-to-draw graphs to summarize data quickly are called
1. exploratory data analysis
2. relative frequency distributions
3. bar charts
4. pie charts

1. The total number of data items with a value less than or equal to the upper limit for the class is given by the
1. frequency distribution
2. relative frequency distribution
3. cumulative frequency distribution
4. cumulative relative frequency distribution

1. Excel's                              can be used to construct a frequency distribution for quantitative data.
1. COUNTIF function
2. SUM function
3. PivotTable Report
4. AVERAGE function

1. 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
1. histogram
2. bar chart
3. stem-and-leaf display
4. pie chart

1. A common graphical presentation of quantitative data is a
1. histogram
2. bar chart
3. relative frequency
4. pie chart

1. When using Excel to create a                                 one must edit the chart to remove the gaps between rectangles.
1. scatter diagram
2. bar chart
3. histogram
4. pie chart

1. A                             can be used to graphically present quantitative data.
1. histogram
2. pie chart
3. stem-and-leaf display

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

1. A(n)                             is a graph of a cumulative distribution.
1. histogram
2. pie chart
3. stem-and-leaf display
4. ogive

1. Excel's Chart Tools can be used to construct a
1. bar chart
2. pie chart
3. histogram
4. All of these can be constructed using Excel's Chart Tools.

1. To construct a bar chart using Excel's Chart Tools, choose                                       as the chart type.
1. column
2. pie
3. scatter
4. line

1. To construct a pie chart using Excel's Chart Tools, choose                                      as the chart type.
1. column
2. pie
3. scatter
4. line

1. To construct a histogram using Excel's Chart Tools, choose                                       as the chart type.
1. column
2. pie

1. scatter
2. line

1. Excel's Chart Tools does not have a chart type for constructing a
1. bar chart
2. pie chart
3. histogram
4. stem-and-leaf display

1. A tabular method that can be used to summarize the data on two variables simultaneously is called
1. simultaneous equations
2. a crosstabulation
3. a histogram
4. a dot plot

1. Excel's                              can be used to construct a crosstabulation.
1. Chart Tools
2. SUM function
3. PivotTable Report
4. COUNTIF function

1. In a crosstabulation
1. both variables must be categorical
2. both variables must be quantitative
3. one variable must be categorical and the other must be quantitative
4. either or both variables can be categorical or quantitative

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

1. a pie chart
2. a histogram
3. a crosstabulation
4. a scatter diagram

1. Excel's                              can be used to construct a scatter diagram.
1. Chart Tools
2. SUM function
3. CROSSTAB function
4. RAND function

1. When the conclusions based upon the aggregated crosstabulation can be completely reversed if we look at the unaggregated data, the occurrence is known as
1. reverse correlation
2. inferential statistics
4. disaggregation

1. Before drawing any conclusions about the relationship between two variables shown in a crosstabulation, you should
1. investigate whether any hidden variables could affect the conclusions
2. construct a scatter diagram and find the trendline
3. develop a relative frequency distribution
4. construct an ogive for each of the variables

1. A histogram is not appropriate for displaying which of the following types of information?

1. frequency
2. relative frequency
3. cumulative frequency
4. percent frequency

1. For stem-and-leaf displays where the leaf unit is not stated, the leaf unit is assumed to equal
1. 0
2. .1
3. 1
4. 10

1. Which of the following graphical methods is not intended for quantitative data?
1. ogive
2. dot plot
3. scatter diagram
4. pie chart

1. Which of the following is least useful in studying the relationship between two variables?
1. trendline
2. stem-and-leaf display
3. crosstabulation
4. scatter diagram

1. The sum of the relative frequencies in any relative frequency distribution always equals
1. the number of observations

b. 1.00

c. 100

d. the number of variables

1. The sum of the frequencies in any frequency distribution always equals
1. the number of observations

b. 1.00

c. 100

d. the number of variables

# 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

1. Refer to Exhibit 2-1. The class width for this distribution
1. is 9
2. is 10
3. is 39, which is: the largest value minus the smallest value or 39 ? 0 ? 39
4. varies from class to class

1. Refer to Exhibit 2-1. The midpoint of the last class is
1. 50
2. 34
3. 35

d. 34.5

1. Refer to Exhibit 2-1. The number of students working 19 hours or less
1. is 80
2. is 100
3. is 180
4. is 300

1. Refer to Exhibit 2-1. The relative frequency of students working 9 hours or less
1. is 20
2. is 100

 c. is 0.95 d.   0.05 60. Refer to Exhibit 2-1. 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 2-1. a. 20% b.   25% c.   75% d.   80% The percentage of students working 10 ? 19 hours is 62. Refer to Exhibit 2-1. a. 20% b.   25% c.   75% d.   80% The percentage of students working 19 hours or less is 63. Refer to Exhibit 2-1. a. 100% b.   75% c.   50% d.   25% The cumulative percent frequency for the class of 30 ? 39 is 64. Refer to Exhibit 2-1. a. is 200 The cumulative frequency for the class of 20 ? 29

1. is 300
2. is 0.75
3. is 0.50

1. 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

1. 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

1. Refer to Exhibit 2-2. The number of industries that are classified as retail is
1. 32
2. 18

c.   0.36

d.   36%

1. Refer to Exhibit 2-2. The relative frequency of industries that are classified as banking is
1. 7

b.   0.07

c.   0.70

d.   0.14

1. Refer to Exhibit 2-2. The percent frequency of industries that are classified as electronics is
1. 10
2. 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

1. Refer to Exhibit 2-3. The class width for this distribution
1. is 5
2. is 6
3. is 20, which is: the largest value minus the smallest value or 20 ? 0 ? 20
4. varies from class to class

1. Refer to Exhibit 2-3. The midpoint of the first class is
1. 10
2. 2

c. 2.5

d. 3

1. Refer to Exhibit 2-3. The number of workers who took less than 11 sick days per month
1. was 15
2. was 200
3. was 185
4. was 65

1. Refer to Exhibit 2-3. The number of workers who took at most 10 sick days per month
1. was 15
2. was 200
3. was 185
4. was 65

1. Refer to Exhibit 2-3. The number of workers who took more than 10 sick days per month
1. was 15
2. was 200
3. was 185
4. was 65

1. Refer to Exhibit 2-3. The number of workers who took at least 11 sick days per month
1. was 15
2. was 200
3. was 185
4. was 65

1. Refer to Exhibit 2-3. The relative frequency of workers who took 10 or fewer sick days
1. was 185
2. was 0.925
3. was 93
4. was 15

1. Refer to Exhibit 2-3. The cumulative relative frequency for the class of 11 ? 15
1. is 199
2. is 0.07
3. is 1

d. is 0.995

1. 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%

1. 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%

1. Refer to Exhibit 2-3. The cumulative frequency for the class of 11 ? 15
1. is 200
2. is 14
3. is 199
4. is 1

# 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.

 Graduate School Business Engineering Others Total Yes 35 42 63 140 No 91 104 65 260 Total 126 146 128 400

1. Refer to Exhibit 2-4. What percentage of the students does not plan to go to graduate school? a. 280

b. 520

1. 65
2. 32

1. Refer to Exhibit 2-4. What percentage of the students' undergraduate major is engineering? a. 292

b. 520

c. 65

d. 36.5

1. 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

1. Refer to Exhibit 2-4. Among the students who plan to go to graduate school, what percentage indicated "Other" majors?

a. 15.75

1. 45
2. 54
3. 35

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