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Statistics

What values could you infer from a boxplot?

The median (the line inside the box, not the mean), the first and third quartiles (the box edges, whose gap is the IQR), the whisker ends and any outliers. Whiskers stop at the most extreme point within 1.5 × IQR of the box, so they show the minimum and maximum only when no outliers are drawn.

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Card 1 of 259. Answer: The median (the line inside the box, not the mean), the first and third quartiles (the box edges, whose gap is the IQR), the whisker ends and any outliers. Whiskers stop at the most extreme point within 1.5 × IQR of the box, so they show the minimum and maximum only when no outliers are drawn.

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The longer answer

The median (the line inside the box), the first and third quartiles (the box edges, spanning the interquartile range, IQR = Q3 − Q1), the whisker ends and any outliers. In Tukey's style, a whisker stops at the most extreme point within 1.5 × IQR of the box and points beyond are drawn singly, so the whiskers reach the minimum and maximum only when no outliers appear.

For 1, 3, 4, 5, 6, 7, 8, 10, 13, 18 and 31, the median is 7, Q1 = 4.5 and Q3 = 11.5, so IQR = 7 and the upper fence is 22. The upper whisker ends at 18; 31 is a lone dot. A median nearer Q1 than Q3 and a longer upper whisker signal right skew.

It hides shape: a bimodal sample and a flat one can share a box, and neither the mean nor the sample size is shown, so overlay the points or use a violin plot. Notches, median ± 1.58 × IQR / √n, help compare medians.

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