Chapter 02

Describing Data: Frequency Tables, Frequency Distributions, and

Graphic Presentation

True / False Questions

A frequency distribution groups data into classes showing the number of observations in each class.

True False

A frequency distribution for qualitative data has class limits.

True False

To summarize the gender of students attending a college, the number of classes in a frequency distribution depends on the number of students.

True False

In frequency distributions, classes are mutually exclusive if each individual, object, or measurement is included in only one category.

True False

In a bar chart, the x-axis is labeled with the values of a qualitative variable.

True False

In a bar chart, the heights of the bars represent the frequencies in each class.

True False

The midpoint of a class, which is also called a class mark, is halfway between the lower and upper limits.

True False

A class interval, or class width, can be determined by subtracting the lower limit of a class from the lower limit of the next higher class.

True False

To convert a frequency distribution to a relative frequency distribution, divide each class frequency by the sum of the class frequencies.

True False

To convert a frequency distribution to a relative frequency distribution, divide each class frequency by the number of classes.

True False

A pie chart is similar to a relative frequency distribution.

True False

A pie chart shows the relative frequency in each class.

True False

To construct a pie chart, relative class frequencies are used to graph the "slices" of the pie.

True False

A cumulative frequency distribution is used when we want to determine how many observations lie above or below certain values.

True False

A frequency polygon is a very useful graphic technique when comparing two or more distributions.

True False

Multiple Choice Questions

Monthly commissions of first-year insurance brokers are $1,270, $1,310, $1,680, $1,380, $1,410, $1,570, $1,180 and $1,420. These figures are referred to as a(n) __________.

Histogram

Raw data

Frequency distribution

Frequency polygon

A small sample of computer operators shows monthly incomes of $1,950, $1,775, $2,060, $1,840, $1,795, $1,890, $1,925, and $1,810. What are these ungrouped numbers called?

Histogram

Class limits

Class frequencies

Raw data

18.When data is collected using a quantitative, ratio variable, what is true about a frequency distribution that summarizes the data?

Upper and lower class limits must be calculated.

A pie chart can be used to summarize the data.

Number of classes is equal to the number of variable's values.

The "5 to the k rule" can be applied.

When data is collected using a qualitative, nominal variable, what is true about a frequency distribution that summarizes the data?

The upper and lower class limits must be calculated.

A pie chart can be used to summarize the data.

The number of classes is equal to the number of variable's values plus 2.

The "5 to the k rule" can be applied.

When data is collected using a qualitative, nominal variable (in other words, male or female), what is true about a frequency distribution that summarizes the data?

The upper and lower class limits must be calculated.

Class midpoints can be computed.

The number of classes corresponds to the number of a variable's values.

The "2 to the k rule" can be applied.

A student was interested in the cigarette smoking habits of college students and collected data from an unbiased random sample of students. The data is summarized in the following table:

Why is the table NOT a frequency distribution?

The number of males does not equal the sum of males that smoke and do not smoke.

The classes are not mutually exclusive.

There are too many classes.

Class limits cannot be computed.

A student was interested in the cigarette smoking habits of college students and collected data from an unbiased random sample of students. The data is summarized in the following table:

What type of chart best represents the frequency table?

Bar chart

Box plot

Scatter plot

Frequency polygon

A student was interested in the cigarette smoking habits of college students and collected data from an unbiased random sample of students. The data is summarized in the following table:

What type of chart best represents relative class frequencies?

Box plot

Pie chart

Scatter plot

Frequency polygon

24. When a class interval is expressed as 100 up to 200, _________________________.

Observations with values of 100 are excluded from the class

Observations with values of 200 are included in the class

Observations with values of 200 are excluded from the class

The class interval is 99

25.For a relative frequency distribution, relative frequency is computed as _____________.

The class width divided by class interval

The class midpoint divided by the class frequency

The class frequency divided by the class interval

The class frequency divided by the total frequency.

26. The relative frequency for a class represents the ________________.

Class width

Class midpoint

Class interval

Percent of observations in the class

27.A group of 100 students was surveyed about their interest in a new International Studies program. Interest was measured in terms of high, medium, or low. In the study, 30 students responded high interest, 40 students responded medium interest, and 30 students responded low interest. What is the relative frequency of students with high interest?

.30

.50

.40

.030

28. A group of 100 students were surveyed about their interest in a new Economics major. Interest was measured in terms of high, medium, or low. In the study, 30 students responded high interest, 50 students responded medium interest, and 20 students responded low interest. What is the best way to illustrate the relative frequency of student interest?

Use a cumulative frequency polygon

Use a box plot

Use a pie chart

Use a frequency table

29.The monthly salaries of a sample of 100 employees were rounded to the nearest $10. They ranged from a low of $1,040 to a high of $1,720. If we want to condense the data into seven classes, what is the most convenient class

interval?

A. $50

$100

$150

$200

30. A student was studying the political party preferences of a university's student population. The survey instrument asked students to identify themselves as a Democrat or a Republican. This question is flawed because:

Students generally don't know their political preferences.

The categories are generally mutually exclusive.

The categories are not exhaustive.

Political preference is a continuous variable.

31.A student was studying the political party preferences of a university's student population. The survey instrument asked students to identify their political preference, for example, Democrat, Republican, Libertarian, or another party. The best way to illustrate the frequencies for each political preference is a __________.

Bar chart

Box plot

Histogram

Frequency polygon

32. A student was studying the political party preferences of a university's student population. The survey instrument asked students to identify their political preference—for example, Democrat, Republican, Libertarian, or another party.

The best way to illustrate the relative frequency distribution is a __________.

Bar chart

Pie chart

Histogram

Frequency polygon

33.What is the following table called?

Histogram

Frequency polygon

Cumulative frequency distribution

Frequency distribution

34. For the following distribution of heights, what are the limits for the class with the greatest frequency?

64 and up to 70

65 and 69

65 and up to 70

69.5 and 74.5

35.In a frequency distribution, the number of observations in a class is called the class ________.

Midpoint

Interval

Array

Frequency

36. Why are unequal class intervals sometimes used in a frequency distribution?

To avoid a large number of empty classes

For the sake of variety in presenting the data

To make the class frequencies smaller

To avoid the need for midpoints

37.The number of employees less than the upper limit of each class at Lloyd's Fast Food Emporium is shown in the following table:

What is it called?

A histogram

A cumulative frequency table

A pie chart

A frequency polygon

38. A sample distribution of hourly earnings in Paul's Cookie Factory is:

The limits of the class with the smallest frequency are:

$6.00 and $9.00

$12.00 and up to $14.00

$11.75 and $14.25

$12.00 and up to $15.00

What is the relative frequency for those salespersons that earn from $1,600 up to $1,800?

.02

.024

.20

.24

To plot a cumulative frequency distribution, the first coordinate would be _________.

X = 0, Y = 600

X = 500, Y = 3

X = 3, Y = 600

X = 600, Y = 0

What is the relative frequency of those salespersons that earn $1,600 or more?

25.5%

27.5%

29.5 %

30.8 %

For the preceding distribution, what is the midpoint of the class with the greatest frequency?

A. 1,400

1,500

1,700

The midpoint cannot be determined.

What is the class interval?

A. 200

300

3,500

400

Refer to the following wage breakdown for a garment factory.

What is the class interval for the preceding table of wages?

$2

$3

$4

$5

45. Refer to the following wage breakdown for a garment factory.

What is the class midpoint for the class with the greatest frequency?

A. $5.50

$8.50

$11.50

$14.50

46.Refer to the following wage breakdown for a garment factory.

What are the class limits for the class with the smallest frequencies?

3.5 and 6.5

4 and up to 7

13 and up to 16

12.5 and 15.5

47.Refer to the following distribution of ages:

For the distribution of ages just shown, what is the relative class frequency for the lowest class?

A. .50

.18

.20

.10

48. Refer to the following distribution of ages:

What is the class interval?

9

10

10.5

11

49.Refer to the following distribution of ages:

What is the class midpoint of the highest class?

54

55

64

65

50. Refer to the following information from a frequency distribution for "heights of college women" recorded to the nearest inch: the first two class midpoints are

62.5" and 65.5". What is the class interval?

1"

2"

2.5 "

3 "

51.Refer to the following information from a frequency distribution for "heights of college women" recorded to the nearest inch: the first two class midpoints are

62.5" and 65.5". What are the class limits for the lowest class?

61 and up to 64

62 and up to 64

62 and 65

62 and 63

52. Refer to the following information from a frequency distribution for "heights of college women" recorded to the nearest inch: the first two class midpoints are

62.5" and 65.5". What are the class limits for the third class?

64 and up to 67

67 and 69

67 and up to 70

66 and 68

Refer to the following distribution:

What is the relative class frequency for the $25 up to $35 class?

.02

.04

.05

.10

Refer to the following distribution:

What is the class midpoint for the $45 up to $55 class?

49

49.5

50

50.5

Refer to the following distribution:

What are the class limits for class with the highest frequency?

55 up to 64

54 up to 64

55 up to 65

55 up to 64.5

year by employees of a manufacturing company:

How many employees were absent between 3 up to 6 days?

31

29

14

2

year by employees of a manufacturing company:

How many employees were absent fewer than six days?

60

31

91 46 year by employees of a manufacturing company:

How many employees were absent six days or more?

8

4

22

31 year by employees of a manufacturing company:

How many employees were absent from 6 up to 12 days?

20

8

12 17

Refer to the following breakdown of responses to a survey of room service in a hotel.

What is the class interval for the frequency table above?

10

20

40

None Apply

Refer to the following breakdown of responses to a survey of room service in a hotel.

What is the class with the greatest frequency?

Not satisfied

Satisfied

Highly satisfied

None Apply

Refer to the following breakdown of responses to a survey of room service in a hotel.

What percent of the responses indicated that customers were satisfied?

A. 40%

33%

50 %

100 %

Refer to the following breakdown of responses to a survey of room service in a hotel.

What type of chart should be used to describe the frequency table?

A pie chart

A bar chart

A histogram A frequency polygon

Refer to the following breakdown of responses to a survey of room service in a hotel.

What type of chart should be used to show relative class frequencies?

A pie chart

A bar chart

A histogram A frequency polygon

Refer to the following breakdown of responses to a survey of "Are you concerned about being tracked while connected to the Internet?"

What is the class interval for the preceding frequency table?

10

20

40

None Apply

Refer to the following breakdown of responses to a survey of "Are you concerned about being tracked while connected to the Internet?"

What is the class with the greatest frequency?

Very concerned

Somewhat concerned

No concern

None Apply

Refer to the following breakdown of responses to a survey of "Are you concerned about being tracked while connected to the Internet?"

What percent of the responses indicated that users were somewhat concerned?

A. 40%

70%

20 %

100 %

What type of chart should be used to describe the frequency table?

A pie chart

A bar chart

A histogram A frequency polygon

What type of chart should be used to show relative class frequencies?

A pie chart

A bar chart

A histogram A frequency polygon

What is the class interval for the preceding frequency table?

10

20

40

None Apply

What is the class with the greatest frequency?

Very confident

Somewhat confident

Not very confident Don't know

What percent of the responses indicated that users were very confident?

A. 63%

21%

45 % 33 %

What type of chart should be used to describe the frequency table?

A pie chart

A bar chart

A histogram A frequency polygon

What type of chart should be used to show relative class frequencies?

A pie chart

A bar chart

A histogram

A frequency polygon

75. A pie chart shows the ______________________.

Relative frequencies of a qualitative variable

Relative frequencies of a quantitative variable

Frequencies of a nominal variable

Frequencies of a ratio variable

Fill in the Blank Questions

76.In constructing a frequency polygon, class frequencies are scaled on the ______ axis.

________________________________________

A frequency distribution for nominal data requires that the categories be ___________________ and _____________________.

________________________________________

For a frequency distribution of quantitative data, if every individual, object, or measurement can be assigned to a class, the frequency distribution is __________.

________________________________________

For a frequency distribution of qualitative data, if the observations can be assigned to only one class, the classes are __________________________.

________________________________________

The number of observations in each class of a frequency distribution is called a ________________________.

________________________________________

81.A ___________ is useful for displaying the relative frequency distribution for a

nominal variable.

________________________________________

To calculate a relative frequency, a class frequency is divided by ___________.

________________________________________

In a relative frequency distribution, the sum of the relative class frequencies is _____________________.

________________________________________

A class relative frequency represents a __________ of the total observations in the class.

________________________________________

A _____ chart is useful for displaying a frequency distribution for a qualitative variable.

________________________________________

86.A _____ chart is useful for displaying a frequency distribution for a nominal variable.

________________________________________

The midpoint of a class interval is also called a class ________.

________________________________________

A table showing the number of observations that have been grouped into each of several classes is called a frequency ________________.

________________________________________

In a cumulative frequency distribution, the percent of the total frequencies that would fall below the upper limit of the highest class would be _________.

________________________________________

Unorganized data is referred to as ________ data.

________________________________________

When classes in a frequency table are constructed so that each observation will fit into only one class, the categories are ______________________.

________________________________________

92.The suggested class interval for a frequency distribution with data ranges from 100 to 220 with 50 observations would be _______.

________________________________________

If the number of observations is 124, calculate the suggested number of classes using the "2 to the k rule."

________________________________________

In a frequency distribution, a class defined as "Under $100" and "$1,000 and over" is called a(n) ____________.

________________________________________

In a deck of cards, a class of all cards that are hearts and a class of all cards that are kings are NOT _____________.

________________________________________

To construct a histogram, the class frequencies are plotted on the ________.

________________________________________

To construct a bar chart, the class frequencies are plotted on the _________.

________________________________________

98.To construct a pie chart, the class frequencies are converted to __________.

________________________________________

99. To summarize the gender of students attending a college in a frequency distribution, a total of at least ______ classes would be required.

________________________________________

100.A ______ chart is useful for displaying a relative frequency distribution.

________________________________________

Essay Questions

20 up to 30

30 up to 40

40 up to 50

50 up to 60

60 up to 70

The class limits for the class 50 up to 60 are _______ and ______.

20 up to 30

30 up to 40

40 up to 50

50 up to 60

60 up to 70

What is the midpoint for the class 40 up to 50? 20 up to 30 30 up to 40 40 up to 50

50 up to 60

60 up to 70

What is the class interval?

The first three class marks for a frequency distribution of "weights of college men" recorded to the nearest pound are 105, 115, and 125.

What is the class interval?

105.The first three class marks for a frequency distribution of "weights of college men" recorded to the nearest pound are 105, 115, and 125.

What is the lower limit for the third class?

106.The first three class marks for a frequency distribution of "weights of college men" recorded to the nearest pound are 105, 115, and 125.

What is the upper limit for the third class?

107.The first three class marks for a frequency distribution of "weights of co llege men" recorded to the nearest pound are 105, 115, and 125.

What are the class limits for the fourth class?

Refer to the following breakdown of responses to a survey of room cleanliness in a hotel.

What is the class interval for the following frequency table?

What is the class with the greatest frequency?

Refer to the following breakdown of responses to a survey of room cleanliness in a hotel.

What percent of the responses indicated that customers were satisfied?

Draw a bar graph that illustrates the preceding frequency table.

Draw a bar graph that illustrates the relative frequencies.

Draw a pie chart that illustrates the relative frequencies.

114.A data set consists of 40 observations. For a quantitative variable, how many classes would you recommend for the frequency distribution?

115.A data set has 100 observations. In the data, a quantitative variable's highest value is 117 and its lowest value is 47. What is the minimum class interval that you would recommend?

116.A data set has 200 observations. In the data, a quantitative variable's highest value is 1080 and its lowest value is 960. What is the minimum class interval that you would recommend?

A data set has 200 observations. In the data, a qualitative variable's highest value is "extremely satisfied" and its lowest value is "extremely dissatisfied." What is the minimum class interval that you would recommend?

The following frequency distribution shows the distribution of delivery times (in days) for swimstuff.com customer orders during the last month.

How many orders were delivered in less than one day?

The following frequency distribution shows the distribution of delivery times (in days) for swimstuff.com customer orders during the last month.

What is the relative frequency for orders delivered in less than one day?

The following frequency distribution shows the distributi on of delivery times (in days) for swimstuff.com customer orders during the last month.

How many orders were delivered in less than three days?

days) for swimstuff.com customer orders during the last month.

What is the relative frequency for orders delivered in less than three days? days) for swimstuff.com customer orders during the last month.

How many orders were delivered in three days or more?

days) for swimstuff.com customer orders during the last month.

What is the relative frequency for orders delivered in three days or more? days) for swimstuff.com customer orders during the last month.

How many orders were delivered from 1 day up to 3 days? days) for swimstuff.com customer orders during the last month.

What is the relative frequency of the orders delivered from 1 day up to 3 days? days) for swimstuff.com customer orders during the last month.

For 300 observations, our rule-of-thumb for number of classes would indicate 9 classes. In this case, what is the class interval and why would it be reasonable to use that class interval and only 6 classes?

What is the difference between a bar chart and a pie chart?

128.What is the difference between a frequency distribution and a cumulative frequency distribution?

129.In a bar chart, why are there spaces between the bars on the horizontal axis?

Chapter 02 Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation Answer Key

True / False Questions

A frequency distribution groups data into classes showing the number of observations in each class.

TRUE

AACSB: Communication

Blooms: Remember

Difficulty: 1 Easy Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Frequency Distribution Concepts

A frequency distribution for qualitative data has class limits.

FALSE

Qualitative data is not numeric, so there cannot be class limits.

AACSB: Communication

Blooms: Remember

Difficulty: 1 Easy

Learning Objective: 02-01 Make a frequency table for a set of data.

Topic: Constructing Frequency Distributions: Qualitative Data

To summarize the gender of students attending a college, the number of classes in a frequency distribution depends on the number of students.

FALSE

Gender is a nominal, qualitative variable that has two values. Therefore, there will only be two classes: male and female.

AACSB: Communication

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-01 Make a frequency table for a set of data.

Topic: Constructing Frequency Distributions: Qualitative Data

In frequency distributions, classes are mutually exclusive if each individual, object, or measurement is included in only one category.

TRUE

AACSB: Communication

Blooms: Analyze

Difficulty: 1 Easy Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Frequency Distribution Concepts

In a bar chart, the x-axis is labeled with the values of a qualitative variable.

TRUE

AACSB: Communication

Blooms: Analyze

Difficulty: 1 Easy Learning Objective: 02-02 Organize data into a bar chart.

Topic: Constructing Frequency Distributions: Qualitative Data

In a bar chart, the heights of the bars represent the frequencies in each class.

TRUE

AACSB: Communication

Blooms: Analyze

Difficulty: 1 Easy Learning Objective: 02-02 Organize data into a bar chart.

Topic: Constructing Frequency Distributions: Qualitative Data

The midpoint of a class, which is also called a class mark, is halfway between the lower and upper limits.

TRUE

AACSB: Communication

Blooms: Remember

Difficulty: 1 Easy Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

A class interval, or class width, can be determined by subtracting the lower limit of a class from the lower limit of the next higher class.

TRUE

AACSB: Communication

Blooms: Remember

Difficulty: 1 Easy

Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

To convert a frequency distribution to a relative frequency distribution, divide each class frequency by the sum of the class frequencies.

TRUE

AACSB: Communication

Blooms: Remember

Difficulty: 1 Easy Learning Objective: 02-05 Understand a relative frequency distribution.

Topic: Relative Frequency Distributions

To convert a frequency distribution to a relative frequency distribution, divide each class frequency by the number of classes.

FALSE

Relative frequencies are computed by dividing class frequencies by the total of the class frequencies.

AACSB: Communication

Blooms: Remember

Difficulty: 1 Easy Learning Objective: 02-05 Understand a relative frequency distribution.

Topic: Relative Frequency Distributions

A pie chart is similar to a relative frequency distribution.

TRUE

AACSB: Communication

Blooms: Analyze

Difficulty: 2 Medium Learning Objective: 02-03 Present a set of data using a pie chart.

Topic: Constructing Frequency Distributions: Qualitative Data

A pie chart shows the relative frequency in each class.

TRUE

AACSB: Communication

Blooms: Analyze

Difficulty: 2 Medium Learning Objective: 02-03 Present a set of data using a pie chart.

Topic: Constructing Frequency Distributions: Qualitative Data

To construct a pie chart, relative class frequencies are used to graph the "slices" of the pie.

TRUE

AACSB: Communication

Blooms: Remember

Difficulty: 1 Easy Learning Objective: 02-03 Present a set of data using a pie chart.

Topic: Constructing Frequency Distributions: Qualitative Data

A cumulative frequency distribution is used when we want to determine how many observations lie above or below certain values.

TRUE

AACSB: Communication

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-07 Construct and interpret a cumulative frequency distribution.

Topic: Cumulative Frequency Distribution

A frequency polygon is a very useful graphic technique when comparing two or more distributions.

TRUE

AACSB: Communication

Blooms: Apply

Difficulty: 1 Easy Learning Objective: 02-06 Present data from a frequency distribution in a histogram or frequency polygon.

Topic: Constructing Frequency Distributions: Quantitative Data

Multiple Choice Questions

Monthly commissions of first-year insurance brokers are $1,270, $1,310, $1,680, $1,380, $1,410, $1,570, $1,180 and $1,420. These figures are referred to as a(n) __________.

Histogram

Raw data

Frequency distribution

Frequency polygon

Histograms, frequency distributions, and frequency polygons all summarize data. The data in the question are individual observations or raw data that are not summarized.

AACSB: Communication

Blooms: Remember

Difficulty: 1 Easy Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

A small sample of computer operators shows monthly incomes of $1,950, $1,775, $2,060, $1,840, $1,795, $1,890, $1,925, and $1,810. What are these ungrouped numbers called?

Histogram

Class limits

Class frequencies

Raw data

Histograms and frequency distributions summarize data. The data in the question are the individual observations that are not summarized.

AACSB: Communication

Blooms: Remember

Difficulty: 1 Easy Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

When data is collected using a quantitative, ratio variable, what is true about a frequency distribution that summarizes the data?

Upper and lower class limits must be calculated.

A pie chart can be used to summarize the data.

Number of classes is equal to the number of variable's values.

The "5 to the k rule" can be applied.

Choices B and C refer to frequency distributions for qualitative variables. For quantitative, ratio variables, the number of classes, the class interval, and class limits must be computed.

AACSB: Analytic

Blooms: Analyze

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

When data is collected using a qualitative, nominal variable, what is true about a frequency distribution that summarizes the data?

The upper and lower class limits must be calculated.

A pie chart can be used to summarize the data.

The number of classes is equal to the number of variable's values plus 2.

The "5 to the k rule" can be applied.

A pie chart is used to show the relative frequency for a qualitative, nominal variable. Choices A and D apply to quantitative variables.

AACSB: Analytic

Blooms: Analyze

Difficulty: 2 Medium Learning Objective: 02-03 Present a set of data using a pie chart.

Topic: Constructing Frequency Distributions: Qualitative Data

When data is collected using a qualitative, nominal variable (in other words, male or female), what is true about a frequency distribution that summarizes the data?

The upper and lower class limits must be calculated.

Class midpoints can be computed.

The number of classes corresponds to the number of a variable's values.

The "2 to the k rule" can be applied.

Gender is a nominal, qualitative variable that has two values. Therefore, the frequency distribution will only have two classes: male and female.

AACSB: Analytic

Blooms: Analyze

Difficulty: 2 Medium Learning Objective: 02-01 Make a frequency table for a set of data.

Topic: Constructing Frequency Distributions: Qualitative Data

Why is the table NOT a frequency distribution?

The number of males does not equal the sum of males that smoke and do not smoke.

The classes are not mutually exclusive.

There are too many classes.

Class limits cannot be computed.

In a frequency distribution, the classes must be mutually exclusive so that each data item can be assigned to only one class. In this example, the classes are not mutually exclusive because a female can be assigned to two classes: females and females who smoke or females who do not smoke.

AACSB: Communication

Blooms: Understand

Difficulty: 2 Medium Learning Objective: 02-01 Make a frequency table for a set of data.

Topic: Constructing Frequency Distributions: Qualitative Data

What type of chart best represents the frequency table?

Bar chart

Box plot

Scatter plot

Frequency polygon

The variables are nominal and qualitative. The frequency table is best presented with a bar chart.

AACSB: Communication

Blooms: Understand

Difficulty: 2 Medium Learning Objective: 02-02 Organize data into a bar chart.

Topic: Constructing Frequency Distributions: Qualitative Data

What type of chart best represents relative class frequencies?

Box plot

Pie chart

Scatter plot

Frequency polygon

The variables are nominal and qualitative. Relative frequencies for a qualitative, nominal variable are best summarized with a pie chart.

AACSB: Communication

Blooms: Understand

Difficulty: 2 Medium Learning Objective: 02-03 Present a set of data using a pie chart.

Topic: Constructing Frequency Distributions: Qualitative Data

When a class interval is expressed as 100 up to 200, _________________________.

Observations with values of 100 are excluded from the class

Observations with values of 200 are included in the class

Observations with values of 200 are excluded from the class

The class interval is 99

Class intervals must be interpreted so they are mutually exclusive. The class interval, 100 up to 200, includes values equal to 100 and less than 200.

AACSB: Communication

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

For a relative frequency distribution, relative frequency is computed as _____________.

The class width divided by class interval

The class midpoint divided by the class frequency

The class frequency divided by the class interval

The class frequency divided by the total frequency.

By definition, relative frequency is computed as class frequency divided by total frequency.

AACSB: Communication

Blooms: Remember

Difficulty: 1 Easy Learning Objective: 02-05 Understand a relative frequency distribution.

Topic: Relative Frequency Distributions

The relative frequency for a class represents the ________________.

Class width

Class midpoint

Class interval

Percent of observations in the class

By definition, relative frequency is computed as class frequency divided by total frequency, which is a percent of the total observations in a class.

AACSB: Communication

Blooms: Remember

Difficulty: 1 Easy Learning Objective: 02-05 Understand a relative frequency distribution.

Topic: Relative Frequency Distributions

A group of 100 students was surveyed about their interest in a new International Studies program. Interest was measured in terms of high, medium, or low. In the study, 30 students responded high interest, 40 students responded medium interest, and 30 students responded low interest. What is the relative frequency of students with high interest?

A. .30

.50

.40

.030

For calculations, 30 of the 100 students have a high interest, or 30/100 = .30.

AACSB: Analytic

Blooms: Apply

Difficulty: 2 Medium Learning Objective: 02-05 Understand a relative frequency distribution.

Topic: Relative Frequency Distributions

A group of 100 students were surveyed about their interest in a new Economics major. Interest was measured in terms of high, medium, or low. In the study, 30 students responded high interest, 50 students responded medium interest, and 20 students responded low interest. What is the best way to illustrate the relative frequency of student interest?

Use a cumulative frequency polygon

Use a box plot

Use a pie chart

Use a frequency table

Interest is a qualitative, nominal variable. The relative frequencies for a qualitative, nominal variable are best summarized with a pie chart.

AACSB: Reflective Thinking

Blooms: Analyze

Difficulty: 2 Medium Learning Objective: 02-03 Present a set of data using a pie chart.

Topic: Constructing Frequency Distributions: Qualitative Data

The monthly salaries of a sample of 100 employees were rounded to the nearest $10. They ranged from a low of $1,040 to a high of $1,720. If we want to condense the data into seven classes, what is the most convenient class interval?

$50

$100

$150

$200

($1720 - 1040)/7 = $97.14. Of the answer choices, a class interval of $100 is closest to 97.14.

AACSB: Analytic

Blooms: Understand

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

A student was studying the political party preferences of a university's student population. The survey instrument asked students to identify themselves as a Democrat or a Republican. This question is flawed because:

Students generally don't know their political preferences.

The categories are generally mutually exclusive.

The categories are not exhaustive.

Political preference is a continuous variable.

The survey is not exhaustive because it does not include all possible party preferences, such as Independent or Libertarian.

AACSB: Communication

Blooms: Analyze

Difficulty: 2 Medium Learning Objective: 02-01 Make a frequency table for a set of data.

Topic: Constructing Frequency Distributions: Qualitative Data

A student was studying the political party preferences of a university's student population. The survey instrument asked students to identify their political preference, for example, Democrat, Republican, Libertarian, or another party.

The best way to illustrate the frequencies for each political preference is a __________.

Bar chart

Box plot

Histogram

Frequency polygon

Political preference is a qualitative, nominal variable. Frequencies for a qualitative, nominal variable are best presented with a bar chart.

AACSB: Communication

Blooms: Analyze

Difficulty: 2 Medium Learning Objective: 02-02 Organize data into a bar chart.

Topic: Constructing Frequency Distributions: Qualitative Data

A student was studying the political party preferences of a university's student population. The survey instrument asked students to identify their political preference—for example, Democrat, Republican, Libertarian, or another party.

The best way to illustrate the relative frequency distribution is a __________.

Bar chart

Pie chart

Histogram

Frequency polygon

Political preference is a qualitative, nominal variable. The relative frequencies for a qualitative, nominal variable are best summarized with a pie chart.

AACSB: Communication

Blooms: Analyze

Difficulty: 2 Medium Learning Objective: 02-03 Present a set of data using a pie chart.

Topic: Constructing Frequency Distributions: Qualitative Data

What is the following table called?

Histogram

Frequency polygon

Cumulative frequency distribution

Frequency distribution

The table is not a graph, such as a histogram or frequency polygon. The table shows the number of people in each class.

AACSB: Communication

Blooms: Remember

Difficulty: 1 Easy Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Frequency Distribution Concepts

For the following distribution of heights, what are the limits for the class with the greatest frequency?

64 and up to 70

65 and 69

65 and up to 70

69.5 and 74.5

The frequency table has three classes with frequencies of 10, 70, and 20. The class 65" up to 70" corresponds with the greatest frequency of 70.

AACSB: Communication

Blooms: Understand

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

In a frequency distribution, the number of observations in a class is called the class ________.

Midpoint

Interval

Array

Frequency

By definition, frequency is the number of observations in a class.

AACSB: Communication

Blooms: Remember

Difficulty: 1 Easy Learning Objective: 02-01 Make a frequency table for a set of data.

Topic: Constructing Frequency Distributions: Qualitative Data

Why are unequal class intervals sometimes used in a frequency distribution?

To avoid a large number of empty classes

For the sake of variety in presenting the data

To make the class frequencies smaller

To avoid the need for midpoints

When constructing frequency distributions, sometimes there are extreme or outlier values. Therefore, there would be several classes with zero frequencies. To better summarize the data, a class would be created with extended limits that would include the classes with zero frequencies and all the outlier or extreme values.

AACSB: Reflective Thinking

Blooms: Analyze

Difficulty: 1 Easy Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

The number of employees less than the upper limit of each class at Lloyd's Fast Food Emporium is shown in the following table:

What is it called?

A histogram

A cumulative frequency table

A pie chart

A frequency polygon

The table shows the number of employees in each class or less. So each class frequency is a cumulative total and the table is a cumulative frequency table.

AACSB: Communication

Blooms: Remember

Difficulty: 2 Medium Learning Objective: 02-07 Construct and interpret a cumulative frequency distribution.

Topic: Cumulative Frequency Distribution

A sample distribution of hourly earnings in Paul's Cookie Factory is:

The limits of the class with the smallest frequency are:

$6.00 and $9.00

$12.00 and up to $14.00

$11.75 and $14.25

$12.00 and up to $15.00

The frequency table has three classes with frequencies of 16, 42, and 10. The class $12 up to $15 corresponds with the smallest frequency of 10.

AACSB: Communication

Blooms: Understand

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

What is the relative frequency for those salespersons that earn from $1,600 up to $1,800?

A. .02

.024

.20

.24

The number 0.20 is found by 24/120. Here, 120 is the total number of salespeople in the distribution.

AACSB: Analytic

Blooms: Understand

Difficulty: 2 Medium Learning Objective: 02-05 Understand a relative frequency distribution.

Topic: Relative Frequency Distributions

To plot a cumulative frequency distribution, the first coordinate would be _________.

X = 0, Y = 600

X = 500, Y = 3

X = 3, Y = 600

X = 600, Y = 0

To plot a cumulative frequency distribution, the first point would show a frequency of zero (Y = 0) at the lower limit of the first class.

AACSB: Analytic

Blooms: Apply

Difficulty: 2 Medium Learning Objective: 02-07 Construct and interpret a cumulative frequency distribution.

Topic: Cumulative Frequency Distribution

What is the relative frequency of those salespersons that earn $1,600 or more?

25.5%

27.5%

29.5 %

30.8 %

The figure of 30.8%, or 37/120, is found by taking the total of the frequencies for $1,600 or more (24 + 9 + 4) and dividing by the total of 120.

AACSB: Communication

Blooms: Understand

Difficulty: 2 Medium Learning Objective: 02-05 Understand a relative frequency distribution.

Topic: Relative Frequency Distributions

For the preceding distribution, what is the midpoint of the class with the greatest frequency?

A. 1,400

1,500

1,700

The midpoint cannot be determined.

The class with the greatest frequency is "1,400 up to 1,600." The class midpoint is the lower limit (1,400) plus one half of the class interval (1/2 × 200 = 100) or 1,400 + 100 = 1,500.

AACSB: Communication

Blooms: Understand

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

Refer to the following distribution of commissions:

What is the class interval?

200

300

3,500

400

The class interval is 200, found by the difference between any consecutive lower or upper class limits.

AACSB: Communication

Blooms: Understand

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

What is the class interval for the preceding table of wages?

$2

$3

$4

$5

The class interval is $3, found by the difference between any consecutive lower or upper class limits.

AACSB: Analytic

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

What is the class midpoint for the class with the greatest frequency?

$5.50

$8.50

$11.50

$14.50

The class with the greatest frequency is "7 up to 10." The class midpoint is the lower limit (7) plus half of the class interval (1/2 × 3 = 1.5) or $7 + 1.5 = $8.50.

AACSB: Analytic

Blooms: Apply

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

What are the class limits for the class with the smallest frequencies?

3.5 and 6.5

4 and up to 7

13 and up to 16

12.5 and 15.5

This class has the lowest frequency with 6 wage earners in the class.

AACSB: Communication

Blooms: Understand

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

For the distribution of ages just shown, what is the relative class frequency for the lowest class?

.50

.18

.20

.10

The answer .20, or 10/50, is found by dividing 10 by the total of 50.

AACSB: Analytic

Blooms: Apply

Difficulty: 2 Medium Learning Objective: 02-05 Understand a relative frequency distribution.

Topic: Relative Frequency Distributions

What is the class interval?

9

10

10.5

11

The class interval is 10, found by the difference between any consecutive lower or upper class limits.

AACSB: Communication

Blooms: Understand

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set. Topic: Constructing Frequency Distributions: Quantitative Data

What is the class midpoint of the highest class?

54

55

64

65

The highest class is "60 up to 70." The class midpoint is the lower limit (60) plus half of the class interval: ½ × 10 = 5, or $60 + 5 = 65.

AACSB: Analytic

Blooms: Apply

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set. Topic: Constructing Frequency Distributions: Quantitative Data

Refer to the following information from a frequency distribution for "heights of college women" recorded to the nearest inch: the first two class midpoints are

62.5" and 65.5". What is the class interval?

1"

2"

2.5 "

3 "

The class interval can be computed as the difference between adjacent class midpoints (65.5 - 62.5 = 3)

AACSB: Communication

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

Refer to the following information from a frequency distribution for "heights of college women" recorded to the nearest inch: the first two class midpoints are

62.5" and 65.5". What are the class limits for the lowest class?

61 and up to 64

62 and up to 64

62 and 65

62 and 63

Based on the class midpoints, the class interval is 3. The class limit for the lowest class would be the class midpoint less one half of the class interval, or

62.5 - (½ × 3) = 61.

AACSB: Analytic

Blooms: Analyze

Difficulty: 3 Hard Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

Refer to the following information from a frequency distribution for "heights of college women" recorded to the nearest inch: the first two class midpoints are

62.5" and 65.5". What are the class limits for the third class?

64 and up to 67

67 and 69

67 and up to 70

66 and 68

Based on the class midpoints, the class interval is 3. The class limit for the lowest class would be the class midpoint less half of the class interval, or 62.5 - (½ × 3) = 61. Then adding the class interval, the lower limit of the second class would be 64 and the lower limit of the third class would be 67. Again, applying the class interval, the upper limit of the third class would be 70.

AACSB: Analytic

Blooms: Analyze

Difficulty: 3 Hard Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

Refer to the following distribution:

What is the relative class frequency for the $25 up to $35 class?

A. .02

.04

.05

.10

The class frequency divided by the total observations: 2/50 = 0.04.

AACSB: Analytic

Blooms: Understand

Difficulty: 2 Medium Learning Objective: 02-05 Understand a relative frequency distribution.

Topic: Relative Frequency Distributions

Refer to the following distribution:

What is the class midpoint for the $45 up to $55 class?

49

49.5

50

50.5

The class midpoint is the lower limit (45) plus half of the class interval ½ × 10 = 5, or 45 + 5 = 50.

AACSB: Analytic

Blooms: Apply

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

Refer to the following distribution:

What are the class limits for class with the highest frequency?

55 up to 64

54 up to 64

55 up to 65

55 up to 64.5

This class with the highest frequency of 20 observations is "55 up to 65."

AACSB: Communication

Blooms: Understand

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

Refer to the following frequency distribution on days absent during a calendar year by employees of a manufacturing company:

How many employees were absent between 3 up to 6 days?

31

29

14

2

From the chart, there are 31 employees who were absent 3 up to 6 days.

AACSB: Communication

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

Refer to the following frequency distribution on days absent during a calendar year by employees of a manufacturing company:

How many employees were absent fewer than six days?

60

31

91

46

To find the number of employees who were absent fewer than six days, add the frequencies for the classes, 0 up to 3 days, and 3 up to 6 days, or 60 + 31 =

91.

AACSB: Analytic

Blooms: Apply

Difficulty: 3 Hard 07 Construct and interpret a cumulative frequency distribution.

Refer to the following frequency distribution on days absent during a calendar year by employees of a manufacturing company:

How many employees were absent six days or more?

8

4

22

31

To find the number of employees who were absent six or more days, add the frequencies for the classes, 6 up to 9 days, and 9 up to 12 days, and 12 up to 15 days, or 14 + 6 + 2 = 22.

AACSB: Analytic

Blooms: Apply

Difficulty: 3 Hard 07 Construct and interpret a cumulative frequency distribution.

How many employees were absent from 6 up to 12 days?

20

8

12

17

To find the number of employees who were absent from 6 up to 12 days, add the frequencies for the classes, 6 up to 9 days, and 9 up to 12 days, or 14 + 6 =

20.

AACSB: Analytic

Blooms: Apply

Difficulty: 3 Hard

07 Construct and interpret a cumulative frequency distribution.

Refer to the following breakdown of responses to a survey of room service in a hotel.

What is the class interval for the frequency table above?

10

20

40

None Apply

There is no class interval for data measured on an ordinal scale.

AACSB: Communication

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-01 Make a frequency table for a set of data.

Topic: Constructing Frequency Distributions: Qualitative Data

Refer to the following breakdown of responses to a survey of room service in a hotel.

What is the class with the greatest frequency?

Not satisfied

Satisfied

Highly satisfied

None Apply

The highly satisfied class has 60 people.

AACSB: Communication

Blooms: Understand

Difficulty: 1 Easy

Learning Objective: 02-01 Make a frequency table for a set of data.

Refer to the following breakdown of responses to a survey of room service in a hotel.

What percent of the responses indicated that customers were satisfied?

A. 40%

33%

50 %

100 %

The answer (33%) is found by dividing the frequency of the satisfied class by the total frequency, or 40/120.

AACSB: Analytic

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-05 Understand a relative frequency distribution.

Topic: Relative Frequency Distributions

Refer to the following breakdown of responses to a survey of room service in a hotel.

What type of chart should be used to describe the frequency table?

A pie chart

A bar chart

A histogram

A frequency polygon

Bar charts can be used to illustrate a frequency table.

AACSB: Analytic

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-02 Organize data into a bar chart.

Refer to the following breakdown of responses to a survey of room service in a hotel.

What type of chart should be used to show relative class frequencies?

A pie chart

A bar chart

A histogram

A frequency polygon

Pie charts can be used to illustrate relative frequencies for an ordinal variable.

AACSB: Analytic

Blooms: Understand

Difficulty: 1 Easy

Learning Objective: 02-03 Present a set of data using a pie chart.

What is the class interval for the preceding frequency table?

10

20

40

None Apply

There is no class interval for data measured on an ordinal scale.

AACSB: Communication

Blooms: Understand

Difficulty: 1 Easy

Learning Objective: 02-01 Make a frequency table for a set of data.

What is the class with the greatest frequency?

Very concerned

Somewhat concerned

No concern

None Apply

The very concerned class has 140 people.

AACSB: Communication

Blooms: Understand

Difficulty: 1 Easy

Learning Objective: 02-01 Make a frequency table for a set of data.

What percent of the responses indicated that users were somewhat concerned?

A. 40%

70%

20 %

100 %

The answer (20%) is found by dividing the frequency of the somewhat concerned class by the total frequency, or 40/200.

AACSB: Analytic

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-05 Understand a relative frequency distribution.

Topic: Relative Frequency Distributions

What type of chart should be used to describe the frequency table?

A pie chart

A bar chart

A histogram

A frequency polygon

Bar charts can be used to illustrate a frequency table.

AACSB: Analytic

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-02 Organize data into a bar chart.

Topic: Constructing Frequency Distributions: Qualitative Data

What type of chart should be used to show relative class frequencies?

A pie chart

A bar chart

A histogram

A frequency polygon

Pie charts can be used to illustrate relative frequencies for an ordinal variable.

AACSB: Analytic

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-03 Present a set of data using a pie chart.

Topic: Constructing Frequency Distributions: Qualitative Data

What is the class interval for the preceding frequency table?

10

20

40

None Apply

There is no class interval for data measured on an ordinal scale.

AACSB: Communication

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-01 Make a frequency table for a set of data.

Topic: Constructing Frequency Distributions: Qualitative Data

What is the class with the greatest frequency?

Very confident

Somewhat confident

Not very confident

Don't know

The Somewhat Confident class with 135 people.

AACSB: Communication

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-01 Make a frequency table for a set of data.

Topic: Constructing Frequency Distributions: Qualitative Data

What percent of the responses indicated that users were very confident?

A. 63%

21%

45 %

33 %

The answer (21%) is found by dividing the frequency of the Very Confident class by the total frequency, or 63/300.

AACSB: Analytic

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-05 Understand a relative frequency distribution.

Topic: Relative Frequency Distributions

What type of chart should be used to describe the frequency table?

A pie chart

A bar chart

A histogram

A frequency polygon

Bar charts can be used to illustrate a frequency table.

AACSB: Analytic

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-02 Organize data into a bar chart.

Topic: Constructing Frequency Distributions: Qualitative Data

What type of chart should be used to show relative class frequencies?

A pie chart

A bar chart

A histogram

A frequency polygon

Pie charts can be used to illustrate relative frequencies for an ordinal variable.

AACSB: Analytic

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-03 Present a set of data using a pie chart.

Topic: Constructing Frequency Distributions: Qualitative Data

A pie chart shows the ______________________.

Relative frequencies of a qualitative variable

Relative frequencies of a quantitative variable

Frequencies of a nominal variable

Frequencies of a ratio variable

Pie charts can be used to illustrate relative frequencies for qualitative variables.

AACSB: Analytic

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-03 Present a set of data using a pie chart.

Topic: Constructing Frequency Distributions: Qualitative Data

Fill in the Blank Questions

In constructing a frequency polygon, class frequencies are scaled on the ______ axis.

Y or vertical (axis)

By definition, the Y or vertical axis is labeled as class frequency, while the X or horizontal axis is labeled with class limits or midpoints.

AACSB: Communication

Blooms: Remember

Difficulty: 1 Easy Learning Objective: 02-06 Present data from a frequency distribution in a histogram or frequency polygon.

Topic: Constructing Frequency Distributions: Quantitative Data

A frequency distribution for nominal data requires that the categories be ___________________ and _____________________.

Exhaustive; mutually exclusive

By definition, every observation must be included in the distribution

(exhaustive) and can belong to only one category or class (mutually exclusive).

AACSB: Communication

Blooms: Understand

Difficulty: 2 Medium

Learning Objective: 02-01 Make a frequency table for a set of data.

For a frequency distribution of quantitative data, if every individual, object, or measurement can be assigned to a class, the frequency distribution is __________.

Exhaustive

Exhaustive means that all individuals or objects can be assigned to a class in a frequency distribution.

AACSB: Communication

Blooms: Remember

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

For a frequency distribution of qualitative data, if the observations can be assigned to only one class, the classes are __________________________.

Mutually exclusive

By definition, every observation can belong to only one category or class.

AACSB: Communication

Blooms: Remember

Difficulty: 2 Medium

Learning Objective: 02-01 Make a frequency table for a set of data.

The number of observations in each class of a frequency distribution is called a

________________________.

Class frequency or frequency

By definition, frequency is the number of times an event occurs within a specific interval.

AACSB: Communication

Blooms: Remember

Difficulty: 1 Easy Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

A ___________ is useful for displaying the relative frequency distribution for a

nominal variable.

Pie chart

In a pie chart, the whole represents 100% that is divided into proportions based on the relative frequencies for each category of a nominal variable.

AACSB: Communication

Blooms: Apply

Difficulty: 2 Medium

Learning Objective: 02-03 Present a set of data using a pie chart.

To calculate a relative frequency, a class frequency is divided by ___________.

The total number of observations

By definition, relative frequency is equal to the class frequency divided by the total of the class frequencies, or the total frequency.

AACSB: Communication

Blooms: Apply

Difficulty: 2 Medium Learning Objective: 02-05 Understand a relative frequency distribution.

Topic: Relative Frequency Distributions

In a relative frequency distribution, the sum of the relative class frequencies is _____________________.

1.00

relative frequency represents a proportion or percentage of the total.

Therefore, the sum of all the relative frequencies must equal the whole, or 1.00.

AACSB: Communication

Blooms: Apply

Difficulty: 2 Medium Learning Objective: 02-05 Understand a relative frequency distribution.

Topic: Relative Frequency Distributions

A class relative frequency represents a __________ of the total observations in the class.

Proportion or percentage

By definition, a proportion or percentage is part of the whole. So, a relative frequency is a class frequency as a percentage or proportion of the total frequency.

AACSB: Communication

Blooms: Apply

Difficulty: 2 Medium Learning Objective: 02-05 Understand a relative frequency distribution.

Topic: Relative Frequency Distributions

A _____ chart is useful for displaying a frequency distribution for a qualitative variable.

Bar

For a frequency distribution, frequencies or counts are clearly illustrated with a bar chart.

AACSB: Communication

Blooms: Apply

Difficulty: 2 Medium Learning Objective: 02-02 Organize data into a bar chart.

Topic: Constructing Frequency Distributions: Qualitative Data

A _____ chart is useful for displaying a frequency distribution for a nominal variable.

Bar

For a frequency distribution, frequencies or counts are clearly illustrated with a bar chart.

AACSB: Communication

Blooms: Apply

Difficulty: 2 Medium Learning Objective: 02-02 Organize data into a bar chart.

Topic: Constructing Frequency Distributions: Qualitative Data

The midpoint of a class interval is also called a class ________.

Mark

By definition, a class midpoint is the same as a class mark.

AACSB: Communication

Blooms: Remember

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

A table showing the number of observations that have been grouped into each of several classes is called a frequency ________________.

Distribution

By definition, organizing data by summarizing frequencies in classes is a frequency distribution.

AACSB: Communication

Blooms: Remember

Difficulty: 1 Easy Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

In a cumulative frequency distribution, the percent of the total frequencies that would fall below the upper limit of the highest class would be _________.

100%

In a cumulative frequency distribution, the last class is the sum of all frequencies for all lower classes, or 100% of all observations.

AACSB: Communication

Blooms: Understand

Difficulty: 2 Medium Learning Objective: 02-07 Construct and interpret a cumulative frequency distribution.

Topic: Cumulative Frequency Distribution

Unorganized data is referred to as ________ data.

Raw or ungrouped

listing of measurements for a sample or population of individuals is considered raw or ungrouped data.

AACSB: Communication

Blooms: Remember

Difficulty: 1 Easy Learning Objective: 02-01 Make a frequency table for a set of data.

Topic: Constructing Frequency Distributions: Qualitative Data

When classes in a frequency table are constructed so that each observation will fit into only one class, the categories are ______________________.

Mutually exclusive

By definition, mutually exclusive means that an observation, like the gender of a person is female, eliminates the possibility that the person is male. In a frequency table, a person cannot be classified as both female and male.

Therefore, the categories are mutually exclusive.

AACSB: Communication

Blooms: Remember

Difficulty: 2 Medium Learning Objective: 02-01 Make a frequency table for a set of data.

Topic: Constructing Frequency Distributions: Qualitative Data

The suggested class interval for a frequency distribution with data ranges from 100 to 220 with 50 observations would be _______.

20

The class interval would be (maximum - minimum)/number of classes. Using the "2 to the k rule," there would be 6 classes. So (220 - 100)/6 = 20.

AACSB: Analytic

Blooms: Apply

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

If the number of observations is 124, calculate the suggested number of classes using the "2 to the k rule."

7 × classes

26 = 64, 27 = 128. Since 124 is less than 128, the rule says that we should use 7 classes.

AACSB: Analytic

Blooms: Understand

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

In a frequency distribution, a class defined as "Under $100" and "$1,000 and over" is called a(n) ____________.

Open class

Both examples do not have specified upper or lower limits. So they are "open classes."

AACSB: Reflective Thinking

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

In a deck of cards, a class of all cards that are hearts and a class of all cards that are kings are NOT _____________.

Mutually exclusive

The king of hearts is included in both classes. It is a king and a heart.

Therefore, the classes are not mutually exclusive.

AACSB: Reflective Thinking

Blooms: Understand

Difficulty: 3 Hard Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Frequency Distribution Concepts

To construct a histogram, the class frequencies are plotted on the ________.

Y or vertical axis

To illustrate a frequency distribution with a histogram, class frequencies are plotted on the vertical axis, and the class limits on the horizontal axis.

AACSB: Communication

Blooms: Remember

Difficulty: 1 Easy Learning Objective: 02-06 Present data from a frequency distribution in a histogram or frequency polygon.

Topic: Constructing Frequency Distributions: Quantitative Data

To construct a bar chart, the class frequencies are plotted on the _________.

Y or vertical axis

To illustrate a frequency distribution with a bar chart, class frequencies are plotted on the vertical axis, and the classes on the horizontal axis.

AACSB: Communication

Blooms: Remember

Difficulty: 1 Easy Learning Objective: 02-02 Organize data into a bar chart.

Topic: Constructing Frequency Distributions: Qualitative Data

To construct a pie chart, the class frequencies are converted to __________.

Relative frequencies

Pie charts are used to show relative frequencies. So class frequencies must be divided by total frequencies to compute relative frequencies.

AACSB: Communication

Blooms: Remember

Difficulty: 1 Easy Learning Objective: 02-03 Present a set of data using a pie chart.

Topic: Constructing Frequency Distributions: Qualitative Data

To summarize the gender of students attending a college in a frequency distribution, a total of at least ______ classes would be required.

Two

For nominal variables, such as gender or color, the number of classes corresponds with the number of values for the nominal variable. A frequency distribution for gender would have two classes: male and female. A frequency distribution of primary colors would have three classes: red, yellow, and blue.

AACSB: Communication

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-01 Make a frequency table for a set of data.

Topic: Constructing Frequency Distributions: Qualitative Data

______ chart is useful for displaying a relative frequency distribution.

Pie

Relative frequencies are a percentage or proportion in relation to the whole. A pie chart shows "slices" in proportion to the whole. So a pie chart is useful for displaying a relative frequency distribution.

AACSB: Communication

Blooms: Apply

Difficulty: 2 Medium Learning Objective: 02-05 Understand a relative frequency distribution.

Topic: Relative Frequency Distributions

Essay Questions

were grouped into a distribution with the following class limits:

20 up to 30

30 up to 40

40 up to 50

50 up to 60

60 up to 70

The class limits for the class 50 up to 60 are _______ and ______.

50, 60

Feedback: By definition, the values are 50 and 60.

AACSB: Communication

Blooms: Understand

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

were grouped into a distribution with the following class limits:

20 up to 30

30 up to 40

40 up to 50

50 up to 60

60 up to 70

What is the midpoint for the class 40 up to 50?

45

Feedback: The class interval is 10, so the midpoint for any class would be half of the class interval added to a class lower limit (in this case, 40 + 5 = 45), or subtracted from a class upper limit (50 - 5 = 45).

AACSB: Analytic

Blooms: Understand

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

were grouped into a distribution with the following class limits:

20 up to 30

30 up to 40

40 up to 50 50 up to 60

60 up to 70

What is the class interval?

10

Feedback: The class interval is the difference between the lower or upper class limits of adjacent classes.

AACSB: Communication

Blooms: Remember

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

What is the class interval?

10

Feedback: The class interval is the difference between the class marks or midpoints of adjacent classes. (115 - 105 = 10, or 125 - 115 = 10).

AACSB: Analytic

Blooms: Apply

Difficulty: 3 Hard Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

What is the lower limit for the third class?

120

Feedback: The class interval is 10. The class marks are the same as the class midpoints. Therefore, the upper and lower limits for a class are the class mark plus or minus half of the class interval. For the third class, the lower limit is 125 - ½(10) = 120.

AACSB: Analytic

Blooms: Apply

Difficulty: 3 Hard Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

What is the upper limit for the third class?

130

Feedback: The class interval is 10. The class marks are the same as the class midpoints. Therefore, the upper and lower limits for a class are the class mark plus or minus half of the class interval. For the third class, the upper limit is 125 + ½(10) = 130.

AACSB: Analytic

Blooms: Apply

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

men" recorded to the nearest pound are 105, 115, and 125.

What are the class limits for the fourth class?

130 up to 140

Feedback: The class interval is 10. The class marks are the same as the class midpoints. Therefore, the upper and lower limits for a class are the class mark plus or minus half of the class interval. For the third class, the upper limit is 125 + ½(10) = 130. The upper limit for the third class becomes the lower limit for the fourth class. The class interval, 10, is then added to get the upper limit for the fourth class.

AACSB: Analytic

Blooms: Analyze

Difficulty: 3 Hard Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

Refer to the following breakdown of responses to a survey of room cleanliness in a hotel.

What is the class interval for the following frequency table?

There is no class interval. The variable is qualitative.

Feedback: There is no class interval for data measured on an ordinal scale.

AACSB: Communication

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-01 Make a frequency table for a set of data.

Topic: Constructing Frequency Distributions: Qualitative Data

Refer to the following breakdown of responses to a survey of room cleanliness in a hotel.

What is the class with the greatest frequency?

Satisfied

Feedback: The satisfied class with 40 individuals.

AACSB: Communication

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-01 Make a frequency table for a set of data.

Topic: Constructing Frequency Distributions: Qualitative Data

Refer to the following breakdown of responses to a survey of room cleanliness in a hotel.

What percent of the responses indicated that customers were satisfied?

50%

Feedback: The satisfied class accounts for 40 of the 80 total individuals.

Therefore, 40/80 (or 50%) of the customers were satisfied.

AACSB: Analytic

Blooms: Understand

Difficulty: 1 Easy Learning Objective: 02-01 Make a frequency table for a set of data.

Topic: Constructing Frequency Distributions: Qualitative Data

Refer to the following breakdown of responses to a survey of room cleanliness in a hotel.

Draw a bar graph that illustrates the preceding frequency table.

Feedback: A graph with appropriate labels on the horizontal (satisfaction) and vertical (frequency) axes. The bar for "satisfied" should be twice as high as the "not satisfied and highly satisfied" categories, and these categories should be equal in height.

AACSB: Communication

Blooms: Apply

Difficulty: 1 Easy Learning Objective: 02-01 Make a frequency table for a set of data.

Topic: Constructing Frequency Distributions: Qualitative Data

Refer to the following breakdown of responses to a survey of room cleanliness in a hotel.

Draw a bar graph that illustrates the relative frequencies.

Feedback: A graph with the appropriate labels on the horizontal (satisfaction) and vertical (relative frequency) axes. Bars should show approximate relative frequencies or percentages. The bar for "satisfied" should be twice as high as the "not satisfied and highly satisfied" categories, and these categories should be equal in height.

AACSB: Communication

Blooms: Apply

Topic: Constructing Frequency Distributions: Qualitative Data

Refer to the following breakdown of responses to a survey of room cleanliness in a hotel.

Draw a pie chart that illustrates the relative frequencies.

Feedback: The pie chart should be divided into three slices. The "satisfied" slice should be one half of the pie, and the "not satisfied" and "highly satisfied" slices should each be one quarter of the pie. The slices should be labeled.

AACSB: Communication

Blooms: Apply

Difficulty: 2 Medium Learning Objective: 02-03 Present a set of data using a pie chart.

Topic: Constructing Frequency Distributions: Qualitative Data

A data set consists of 40 observations. For a quantitative variable, how many classes would you recommend for the frequency distribution?

Six classes

Feedback: 26 = 64, since 40 is less than 64, the rule says that we should use 6 classes.

AACSB: Analytic

Blooms: Apply

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

A data set has 100 observations. In the data, a quantitative variable's highest value is 117 and its lowest value is 47. What is the minimum class interval that you would recommend?

The intermediate answer is 7 classes. The difference between the high and low is 70. So, the class interval is 10.

Feedback: The class interval would be (maximum - minimum)/number of classes. Using the "2 to the k rule," there would be 7 classes (100 is less than 27 = 128. So (117 - 47)/7 = 10.

AACSB: Analytic

Blooms: Apply

Difficulty: 3 Hard Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

A data set has 200 observations. In the data, a quantitative variable's highest value is 1080 and its lowest value is 960. What is the minimum class interval that you would recommend?

The intermediate answer is 8 classes. The difference between the high and low is 120. So, the class interval is 15.

Feedback: The class interval would be (maximum - minimum)/number of classes. Using the "2 to the k rule," there would be 8 classes (200 is less than 28 = 256. So (1080 - 960)/8 = 15.

AACSB: Analytic

Blooms: Apply

Difficulty: 3 Hard Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

A data set has 200 observations. In the data, a qualitative variable's highest value is "extremely satisfied" and its lowest value is "extremely dissatisfied." What is the minimum class interval that you would recommend?

There is no class interval because the variable is qualitative, not quantitative.

Feedback: Qualitative data does not have class intervals or class limits.

AACSB: Reflective Thinking

Blooms: Analyze

Difficulty: 3 Hard Learning Objective: 02-01 Make a frequency table for a set of data.

Topic: Constructing Frequency Distributions: Qualitative Data

The following frequency distribution shows the distribution of delivery times (in days) for swimstuff.com customer orders during the last month.

How many orders were delivered in less than one day?

150

Feedback: For the first class, 0 up to 1 day, there are 150 deliveries.

AACSB: Analytic

Blooms: Apply

Topic: Constructing Frequency Distributions: Quantitative Data

What is the relative frequency for orders delivered in less than one day?

0.50

Feedback: For the first class, 0 up to 1 day, the relative frequency is 150 divided by the total, 300. Therefore 150/300, or 0.5, is the relative frequency for the first class.

AACSB: Analytic

How many orders were delivered in less than three days?

255

Feedback: The first three classes account for all the deliveries of less than three days. So summing 150, 60, and 45, there were 255 deliveries of less than three days.

AACSB: Analytic

Blooms: Apply

Topic: Constructing Frequency Distributions: Quantitative Data

What is the relative frequency for orders delivered in less than three days?

0.85

Feedback: The first three classes account for all the deliveries of less than three days. So summing 150, 60, and 45, there were 255 deliveries of less than three days. The relative frequency would be 255/300, or 0.85.

AACSB: Analytic

days) for swimstuff.com customer orders during the last month.

How many orders were delivered in three days or more?

45

Feedback: The three classes, 3 up to 4, 4 up to 5, and 5 up to 6, account for all the deliveries of three days or more. So summing 30, 10, and 5, there were 45 deliveries of three days or more.

AACSB: Analytic

Blooms: Apply

Topic: Constructing Frequency Distributions: Quantitative Data

What is the relative frequency for orders delivered in three days or more?

0.15

Feedback: The three classes, 3 up to 4, 4 up to 5, and 5 up to 6, account for all the deliveries of three days or more. So summing 30, 10, and 5, there were 45 deliveries of three days or more. The relative frequency is 45/300, or 0.15.

AACSB: Analytic

days) for swimstuff.com customer orders during the last month.

How many orders were delivered from 1 day up to 3 days?

105

Feedback: The two classes, 1 up to 2, and 2 up to 3, account for all the deliveries from 1 up to 3 days. So summing 60 and 45, there were 105 deliveries from 1 up to 3 days.

AACSB: Analytic

Blooms: Apply

Difficulty: 2 Medium Learning Objective: 02-04 Create a frequency distribution for a data set. Topic: Constructing Frequency Distributions: Quantitative Data

What is the relative frequency of the orders delivered from 1 day up to 3 days?

0.35.

Feedback: The two classes, 1 up to 2, and 2 up to 3, account for all the deliveries from 1 up to 3 days. So summing 60 and 45, there were 105 deliveries from 1 up to 3 days. The relative frequency is 105/300, or 0.35.

AACSB: Analytic

Blooms: Apply Difficulty: 2 Medium

For 300 observations, our rule-of-thumb for number of classes would indicate 9 classes. In this case, what is the class interval and why would it be reasonable to use that class interval and only 6 classes?

The class interval is 1 day. The class interval would be reasonable because that is the level of detail that the company uses to measure delivery time. The number of classes would be limited to 6 because there are no deliveries that take six days or more.

AACSB: Reflective Thinking

Blooms: Analyze

Difficulty: 3 Hard Learning Objective: 02-04 Create a frequency distribution for a data set.

Topic: Constructing Frequency Distributions: Quantitative Data

What is the difference between a bar chart and a pie chart?

A bar chart shows the frequency for the distribution of a qualitative variable. A pie chart shows the relative frequency for the distribution of a qualitative variable. The pie chart is also a great way to make a visual message of the proportions that each variable contributes to the total observations.

AACSB: Reflective Thinking

Blooms: Analyze

Difficulty: 3 Hard Learning Objective: 02-01 Make a frequency table for a set of data.

Topic: Constructing Frequency Distributions: Qualitative Data

What is the difference between a frequency distribution and a cumulative frequency distribution?

frequency distribution shows the number of observations in each class. A cumulative frequency distribution shows the sum of the number of observations in a class plus all lower-ranked or -valued classes.

AACSB: Reflective Thinking

Blooms: Analyze

Difficulty: 3 Hard Learning Objective: 02-07 Construct and interpret a cumulative frequency distribution.

Topic: Cumulative Frequency Distribution

In a bar chart, why are there spaces between the bars on the horizontal axis?

bar chart shows the frequency distribution of a qualitative variable. A qualitative variable is discrete and not continuous. Therefore, placing a space between each bar reflects the fact that a qualitative variable is not continuous.

AACSB: Reflective Thinking

Blooms: Analyze

Difficulty: 3 Hard Learning Objective: 02-01 Make a frequency table for a set of data.

Topic: Constructing Frequency Distributions: Qualitative Data

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