Question 1

When data is collected using a qualitative, nominal variable, what is true about a frequency distribution that summarizes the data?
A)The upper and lower class limits must be calculated.
B)A pie chart can be used to summarize the data.
C)The number of classes is equal to the number of variable's values plus 2.
D)The "5 to the k rule" can be applieD.

Accepted Answer

Since qualitative nominal variables do not have numerical values, the frequency distribution can be summarized using a pie chart. Therefore, option B is the correct choice. A and C are incorrect because class limits and number of classes are not applicable to nominal variables. The "5 to the k rule" (option D) is applicable only to numerical data, and is not relevant in this case.

Question 2

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

Accepted Answer

Classes in frequency distributions are designed to group data into distinct categories that do not overlap, so each value is included in only one class.

Question 3

A pie chart is similar to a relative frequency distribution.

Accepted Answer

Both a pie chart and a relative frequency distribution show the proportion or percentage of different categories in a data set. The main difference is that a pie chart uses a circular shape and colors to emphasize the visual representation, while a relative frequency distribution typically uses a table or histogram to display the frequencies or percentages.

Question 4

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

Accepted Answer

In a bar chart, the x-axis is typically labeled with the names or categories of a qualitative variable, while the y-axis shows the frequency or count of each category.

Question 5

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) __________.
A)Histogram
B)Raw data
C)Frequency distribution
D)Frequency polygon

Accepted Answer

These figures represent individual observations or measurements collected from a study or survey, which are not yet organized into a table, graph, or chart. This unprocessed form of data collection is known as raw data.

Question 6

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

Accepted Answer

The definition of the midpoint or class mark is that it is halfway between the lower and upper limits of a class interval. Therefore, the statement is true.

Question 7

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?
A)Histogram
B)Class limits
C)Class frequencies
D)Raw data

Accepted Answer

These ungrouped numbers are called raw data, as they have not been organized into classes or categories. A histogram represents grouped data, class limits are the boundaries of a class in grouped data, and class frequencies are the number of observations within a class in grouped data.

Question 8

A pie chart shows the relative frequency in each class.

Accepted Answer

A pie chart displays the distribution of categories as relative sizes of wedge-shaped sections of a circular chart, making it an effective tool for showing relative frequency or proportion of each category.

Question 9

A frequency distribution for qualitative data has class limits.

Accepted Answer

A frequency distribution for qualitative data uses categories or classes, not numerical class limits, which are used for quantitative data.

Question 10

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

Accepted Answer

This is the correct method for converting a frequency distribution to a relative frequency distribution.

Question 11

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.

Accepted Answer

A class interval or class width is the difference between the upper and lower limits of a class. To determine this, we subtract the lower limit of a class from the upper limit of the same class.

Question 12

When data is collected using a quantitative, ratio variable, what is true about a frequency distribution that summarizes the data?
A)Upper and lower class limits must be calculated.
B)A pie chart can be used to summarize the data.
C)Number of classes is equal to the number of variable's values.
D)The "5 to the k rule" can be applieD.

Accepted Answer

When collecting data using a quantitative, ratio variable, upper and lower class limits must be calculated for a frequency distribution. This is necessary to properly group the data into classes for a frequency distribution. Choice B is incorrect because a pie chart is not appropriate for summarizing quantitative, ratio data. Choice C is incorrect because the number of classes for a frequency distribution should be determined using an appropriate method such as the Sturges formula or the Freedman-Diaconis rule, not simply the number of variable values. Choice D is incorrect because the "5 to the k rule" is a guideline for determining sample size in statistical analysis, not for summarizing data in a frequency distribution.

Question 13

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

Accepted Answer

To convert a frequency distribution to a relative frequency distribution, divide each class frequency by the total number of observations (not the number of classes).

Question 14

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

Accepted Answer

This statement is true.

Question 15

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

Accepted Answer

The number of classes in a frequency distribution does not depend on the number of students, but rather on the desired level of detail and the range of values being analyzed.

Question 16

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

Accepted Answer

In a bar chart, the height of each bar represents a numerical value, which could be a frequency, count, or any other measure. In some cases, the bars may represent proportions or percentages, but they still represent a quantitative value.

Question 17

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?
A)The upper and lower class limits must be calculated.
B)Class midpoints can be computed.
C)The number of classes corresponds to the number of a variable's values.
D)The "2 to the k rule" can be applieD.

Accepted Answer

When collecting data using a qualitative, nominal variable, such as gender (male or female), the number of classes in the frequency distribution corresponds to the number of values the variable can take on (2 in the case of male or female). Class limits and midpoints cannot be computed since the data is not numeric. The "2 to the k rule" is not relevant in this situation. Therefore, option C is the best choice.

Question 18

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

Accepted Answer

Pie charts represent relative frequencies by dividing a circle into slices based on the relative size of each class.

Question 19

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

Accepted Answer

A frequency polygon is a graph that shows the distribution of data by connecting the midpoints of each interval on a histogram. It is a useful technique for comparing multiple distributions as it allows for easy visualization and comparison of the data.

Question 20

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

Accepted Answer

A cumulative frequency distribution allows us to see the total number of observations that fall at or below a certain value. This is useful when comparing the distribution of data between different groups or when trying to understand the overall pattern of a dataset.

Quiz 2: Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation

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