What are the components of a box-and-whisker plot, and what do they represent?

• A. Box from Q1 to Q3; median line inside; whiskers extend to minimum and maximum non-outlier values; outliers plotted separately.
• B. Box from Q2 to Q4; whiskers show mean
• C. Whiskers extend to absolute min and max including outliers
• D. Box shows only quartiles, no whiskers

Answer: (A)

Box-and-whisker plots summarize distribution by showing the central 50% of the data in a box from the first quartile (Q1) to the third quartile (Q3), with a line inside marking the median. The whiskers reach the smallest and largest data values that are not considered outliers, and any outliers are shown separately as individual points. This arrangement conveys the data’s spread, any skew (via the median’s position inside the box), and the presence of outliers.

Describing the box as spanning Q2 to Q4 would be incorrect, since those are the median and upper quartile, not the typical box extent. Having whiskers that show the mean isn’t standard for box plots, and extending whiskers to include outliers would hide those unusual values. A box plot with only quartiles and no whiskers would omit the useful sense of overall spread and potential outliers.