Which graphical representation shows the median, an interquartile range box, and whiskers?

Which graphical representation shows the median, an interquartile range box, and whiskers?

• A. Histogram
• B. Boxplot
• C. Scatter plot
• D. Stem-and-leaf plot

Answer: (B)

When you want a compact summary of a distribution that highlights center and spread using quartiles, the boxplot is the appropriate choice. In a boxplot, the median is shown as a line inside the central box. The box itself spans from the first quartile (Q1) to the third quartile (Q3), representing the interquartile range. The whiskers extend from the box to show the range of the data beyond the middle 50%, often up to a defined limit like 1.5 times the IQR, with outliers plotted separately. This combination of features—median line, IQR box, and whiskers—is unique to boxplots, which is why it matches the description perfectly. Histograms show frequency by bin height and don’t display a median or IQR; scatter plots show relationships between two variables; stem-and-leaf plots show distribution while preserving data values but don’t present a labeled median with whiskers.

When you want a compact summary of a distribution that highlights center and spread using quartiles, the boxplot is the appropriate choice. In a boxplot, the median is shown as a line inside the central box. The box itself spans from the first quartile (Q1) to the third quartile (Q3), representing the interquartile range. The whiskers extend from the box to show the range of the data beyond the middle 50%, often up to a defined limit like 1.5 times the IQR, with outliers plotted separately. This combination of features—median line, IQR box, and whiskers—is unique to boxplots, which is why it matches the description perfectly. Histograms show frequency by bin height and don’t display a median or IQR; scatter plots show relationships between two variables; stem-and-leaf plots show distribution while preserving data values but don’t present a labeled median with whiskers.