Which statistic is most appropriate for summarizing a data set with categorical observations?

• A. Mean.
• B. Mode.
• C. Median.
• D. Variance.

Answer: (B)

When observations are categorical, you want to identify the category that occurs most often. That measure is the mode. It directly reflects the most frequent category and does not rely on numerical values or arithmetic operations, which don’t make sense for categories like colors, brands, or yes/no responses.

Mean and median require numeric data and an implied order or spacing, which categorical data don’t have. You’d be forced to assign numbers or ranks to categories, but those numbers don’t carry a real, meaningful distance between categories, so the resulting “average” wouldn’t be meaningful. Variance is a measure of spread around a mean and depends on numerical values as well, so it isn’t appropriate for categorical data.

So the mode is the best summary because it cleanly identifies the most common category without imposing a false sense of measurement on non-numeric data. For example, if the data are favorite fruit and apples appear most often, the mode is apples, which accurately communicates the central tendency of the qualitative data.