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Quiz: Displaying Categorical Data

Test your understanding of frequency tables, bar graphs, pie charts, and two-way tables with these review questions.

1. What does a frequency table display?

  1. The relationship between two quantitative variables
  2. Each category and the count of how many times it appears
  3. The average value for each category
  4. The percentage of data that are outliers
Show Answer

The correct answer is B. A frequency table organizes categorical data by listing each category and counting how many times it appears (its frequency). This makes it easy to see which categories are most and least common. The total at the bottom should equal the number of observations.

Concept Tested: Frequency Table

2. In a survey of 80 students, 20 prefer pizza. What is the relative frequency for pizza?

  1. 20
  2. 0.25
  3. 4.0
  4. 80
Show Answer

The correct answer is B. Relative frequency is calculated by dividing the frequency by the total: 20/80 = 0.25 (or 25%). Relative frequency expresses each category's count as a proportion or percentage of the total, allowing for fair comparisons across different sample sizes.

Concept Tested: Relative Frequency

3. Which type of graph is most appropriate for comparing the frequencies of different categorical responses?

  1. Histogram
  2. Scatterplot
  3. Bar graph
  4. Stemplot
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The correct answer is C. Bar graphs are ideal for displaying categorical data, with each category represented as a bar whose height corresponds to its frequency or relative frequency. The bars are separated by gaps to emphasize that categories are distinct. Histograms and stemplots are used for quantitative data.

Concept Tested: Bar Graph

4. When is a pie chart most effective?

  1. When comparing many categories with similar frequencies
  2. When you have a small number of categories and want to show parts of a whole
  3. When displaying quantitative data
  4. When you need to make precise comparisons between categories
Show Answer

The correct answer is B. Pie charts work well when you have a small number of categories (ideally 5 or fewer) and want to show how categories relate to the whole. They become hard to read with many categories or when slices have similar sizes. For precise comparisons, bar graphs are usually better.

Concept Tested: Pie Chart

5. In a two-way table, what do the marginal distributions represent?

  1. The conditional distributions for each category
  2. The distribution of one variable alone, found in the margins of the table
  3. The association between the two variables
  4. Only the outliers in the data
Show Answer

The correct answer is B. Marginal distributions show the distribution of one variable alone and are found in the margins (edges) of a two-way table. They are called "marginal" because they appear in the margins. To find marginal relative frequencies, divide each marginal total by the grand total.

Concept Tested: Marginal Distribution

6. To calculate a conditional distribution of one variable given a specific value of another variable, you should:

  1. Divide each cell by the grand total
  2. Divide each cell in a row or column by that row's or column's total
  3. Add all the cells together
  4. Subtract the row total from the column total
Show Answer

The correct answer is B. For conditional distributions, you focus on one row (or column) and calculate relative frequencies within that row (or column) by dividing by the row (or column) total. This differs from marginal distributions, where you divide by the grand total.

Concept Tested: Calculating Conditionals

7. If two categorical variables have an association, what can we observe?

  1. The marginal distributions are identical
  2. The conditional distributions are different across levels
  3. The variables must have a cause-and-effect relationship
  4. All frequencies in the two-way table are equal
Show Answer

The correct answer is B. When two categorical variables are associated, their conditional distributions differ across levels. If knowing the value of one variable helps predict the other, there is evidence of association. However, association does not prove causation.

Concept Tested: Association

8. A strong positive association between two ordinal categorical variables means:

  1. High values of one variable tend to go with high values of the other
  2. The variables are completely independent
  3. High values of one variable tend to go with low values of the other
  4. The conditional distributions are identical
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The correct answer is A. A positive association means that high values (or certain categories) of one variable tend to occur with high values of the other variable. For example, higher education levels might be associated with higher income categories. A negative association would show the opposite pattern.

Concept Tested: Positive Association

9. What does cumulative frequency show?

  1. The average frequency across all categories
  2. A running total that adds up frequencies as you move through ordered categories
  3. The frequency of the most common category
  4. The difference between the highest and lowest frequencies
Show Answer

The correct answer is B. Cumulative frequency is a running total that adds up frequencies as you move through categories. It works best when categories have a natural order, such as letter grades. It answers questions like "How many students earned a B or higher?"

Concept Tested: Cumulative Frequency

10. When comparing conditional distributions and observing only small differences between groups, what should you conclude about the strength of association?

  1. There is a strong association
  2. There is no relationship whatsoever
  3. There is a weak association or possibly no meaningful association
  4. The data must contain errors
Show Answer

The correct answer is C. When conditional distributions show only small differences, the association is weak. Small differences might just be due to random variation rather than a genuine relationship. We need to consider whether differences are big enough to be meaningful, which formal hypothesis testing can later help determine.

Concept Tested: Strength of Association