On a graph comparing categories, the area of the purple rectangle corresponds to which of the following?

• A. The mean value of a quantitative variable for that category ($\mu$ or $\mathrm{x̅}$)
• B. The correlation between two quantitative variables ($r$)
• C. The standard deviation of the data set ($\sigma$ or $s$)
• D. The frequency or proportion of a qualitative category represented by the rectangle ($p$ or $\frac{n}{N}$)

Answer: (D)

Verified step by step guidance

1. Understand that in a graph comparing categories, especially in bar charts or similar visualizations, the area of a rectangle often represents a quantity related to the category it corresponds to.
2. Recall that the mean value of a quantitative variable is typically represented by a point or a line, not by the area of a rectangle.
3. Recognize that correlation between two quantitative variables is usually shown by scatterplots or correlation coefficients, not by areas of rectangles.
4. Know that the standard deviation is a measure of spread or variability and is not represented by the area of a rectangle in category comparison graphs.
5. Conclude that the area of the purple rectangle corresponds to the frequency or proportion of the qualitative category it represents, as area visually encodes how large or common that category is relative to others.