At a campus political debate, a sample of audience members was asked to state whether they voted in the last Presidential election. The responses are shown in the following table:

Voted Frequency
Yes 45
No 12
Prefer not to answer 79

How would I best display this data? Select all that apply.

Question

At a campus political debate, a sample of audience members was asked to state whether they voted in the last Presidential election. The responses are shown in the following table:

Voted	Frequency
Yes	45
No	12
Prefer not to answer	79

How would I best display this data? Select all that apply.

BlackTom AI · Accepted Answer

Categorical data with three response categories (Yes, No, Prefer not to answer) are best displayed using plots that show counts or proportions for each category.

1. Relevant knowledge points and concepts
- This dataset is a single categorical (nominal) variable with three levels. Appropriate visual displays for single categorical variables include bar graphs, pie charts, and mosaic plots. Histograms and scatterplots are intended for quantitative data; clustered bar graphs are used when comparing categories across a second categorical variable.

2. Step-by-step reasoning
- Determine the type of variable: the responses are categories (voted: Yes/No/Prefer not to answer), not numeric measurements. Therefore choose displays that represent category frequencies or proportions.
- From the table, compute totals and proportions to illustrate what a bar graph or mosaic plot would show.

3. Calculations (all intermediate steps)
- Sum of frequencies: 45 + 12 + 79 = 136.
- Proportion Yes = 45 / 136 = 0.330882 ≈ 33.09% (or 33.1%).
- Proportion No = 12 / 136 = 0.088235 ≈ 8.82% (or 8.8%).
- Proportion Prefer not to answer = 79 / 136 = 0.580882 ≈ 58.09% (or 58.1%).

4. Why the correct answers are correct
- Bar graph: Displays each category as a separate bar whose height equals the frequency (or proportion). It clearly communicates the relative sizes 45, 12, and 79 and is standard for single categorical variables.
- Mosaic plot: Uses area (width × height) to represent proportions of categorical data; for a single categorical variable a mosaic will show the relative shares of each response and is an appropriate alternative to a bar chart for displaying category proportions.

5. Why the other options are incorrect
- Scatterplot: Requires two numerical variables to show relationships; not appropriate for a single categorical variable.
- Clustered bar graph: Useful when comparing category counts across levels of a second categorical variable (e.g., voted by gender). With only one categorical variable, clustering is unnecessary and would be misleading.
- Histogram: Intended for continuous numeric data binned into intervals; not appropriate for discrete categories like vote responses.

6. Conclusion
- The best displays for this single categorical variable are Bar graph and Mosaic plot, which matches the provided correct answers: Bar graph and Mosaic plot.

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