Q: If a pie chart is constructed for a data set with five categories, and one category has a relative frequency of $$0.25$$, what is the degree measure of the corresponding sector?

$$0.25 \times 360^\circ = 90^\circ$$

Question 1

Which of the following best describes a frequency distribution for qualitative data?

Accepted Answer

A table that lists each category and the number of occurrences for each category.

Question 2

Suppose a survey of 200 students found that 80 prefer online classes, 60 prefer in-person classes, and 60 have no preference. What is the relative frequency of students who prefer in-person classes?

Accepted Answer

$$\frac{60}{200} = 0.30$$

Question 3

A bar graph is constructed by:

Accepted Answer

Labeling each category on one axis and the frequency or relative frequency on the other axis, with rectangles of equal width for each category.

Question 4

Which of the following is a key difference between a bar graph and a Pareto chart?

Accepted Answer

A Pareto chart arranges bars in decreasing order of frequency or relative frequency.

Question 5

A pie chart is most appropriate for which type of data?

Accepted Answer

Qualitative data where the emphasis is on showing the part-to-whole relationship.

Question 6

If a pie chart is constructed for a data set with five categories, and one category has a relative frequency of $$0.25$$, what is the degree measure of the corresponding sector?

Accepted Answer

$$0.25 	imes 360^\circ = 90^\circ$$

Question 7

Which of the following statements about bar graphs is FALSE?

Accepted Answer

The bars in a bar graph should touch each other to show continuity.

Question 8

A side-by-side bar graph is most useful when:

Accepted Answer

Comparing the same categories across two or more groups or years.

Question 9

In a survey, 40% of respondents chose 'Option A', 35% chose 'Option B', and 25% chose 'Option C'. Which graphical display would best emphasize the comparison between 'Option A' and 'Option B'?

Accepted Answer

A bar graph

Question 10

Which of the following is a potential pitfall when constructing a bar graph?

Accepted Answer

Starting the scale at a value other than zero can misrepresent the data.

Question 11

A frequency distribution for a qualitative variable must always:

Accepted Answer

List all possible categories and the number of occurrences for each.

Question 12

If the sum of the relative frequencies in a distribution is $$0.98$$, what is the most likely explanation?

Accepted Answer

Rounding error in the calculation of relative frequencies.

Question 13

Which of the following is NOT a reason to use a Pareto chart?

Accepted Answer

To display the relationship between two quantitative variables.

Question 14

A researcher wants to compare the distribution of favorite ice cream flavors among children and adults. Which graphical method is most appropriate?

Accepted Answer

Side-by-side bar graph

Question 15

Which of the following is a correct interpretation of a relative frequency of $$0.25$$ for a category in a data set of 200 observations?

Accepted Answer

50 observations fall into that category.

Organizing and Summarizing Qualitative Data

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