A local university is collecting data on the status of alumni from their social work M.S. program. A random sample of 300 alumni were slected and asked:

Explanatory variable: Are you currently a licensed social worker?

Response variable: Are you currently working as a social worker?

What graph(s) would be appropriate? Select all that apply.

Question

A local university is collecting data on the status of alumni from their social work M.S. program. A random sample of 300 alumni were slected and asked:

Explanatory variable: Are you currently a licensed social worker?

Response variable: Are you currently working as a social worker?

What graph(s) would be appropriate? Select all that apply.

BlackTom AI · Accepted Answer

Both variables are categorical (yes/no), so visualizations that display relationships between two categorical variables are appropriate: a mosaic plot and a clustered (side-by-side) bar graph.

1) Relevant knowledge points and concepts
- Variable types: Explanatory = licensed social worker (categorical: Yes/No), Response = working as a social worker (categorical: Yes/No).
- For two categorical variables, useful graphs show joint or conditional distributions: contingency tables, mosaic plots, grouped (clustered) bar charts, or stacked bar charts. Graphs for quantitative data (histogram, scatterplot, boxplot) are not appropriate.

2) Step-by-step reasoning
- Determine what you want to display: the relationship (association) between licensing status and working status. That requires a bivariate categorical display.
- Mosaic plot: represents the contingency table with rectangle areas proportional to cell counts (or proportions). The widths represent marginal proportions of one variable and the heights represent conditional proportions of the other, so cell areas encode joint frequencies—good for seeing association patterns.
- Clustered bar graph: for each category of the explanatory variable (licensed vs. not), place side-by-side bars showing counts or proportions for the response variable (working vs. not). This allows direct comparison of response distributions across licensing groups.

3) Intermediate/constructive details
- If 300 alumni sampled, compute a 2×2 table of counts. A mosaic plot will scale each cell area = (cell count)/300. A clustered bar chart would show two clusters (licensed, not licensed), each with two bars whose heights = cell count or proportion (cell count / column or row total).

4) Why the correct answers are correct
- Mosaic plot visually encodes joint frequencies and makes association evident via area differences. Clustered bar graph places comparable bars side-by-side so differences in working rates by licensing status are easy to read.

5) Why other options are incorrect
- Histogram: for continuous numeric variables, not categorical.
- Scatterplot: for two quantitative variables, not categorical.
- Stacked box plot: boxplots summarize distributions of numeric variables; “stacked box plot” is not a standard tool for two categorical variables.
- Bar graph (single): a single-variable bar chart could summarize one variable only; it does not by itself show the bivariate relationship. The clustered bar graph is the correct form when comparing a response across categories of an explanatory variable.

6) Conclusion
Mosaic plot and clustered bar graph are the appropriate choices. This matches the provided correct answer: Mosaic plot and Clustered bar graph.

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