Box Plots, Outliers and Comparing Distributions

A box runs from \(Q_1\) to \(Q_3\), with a line at the median. Whiskers reach the most extreme non-outlying observations; mark outliers with crosses.

Here \(Q_1=8\), median \(=11\), \(Q_3=14\) and \(\operatorname{IQR}=6\). The upper fence is \(14+1.5(6)=23\); the observation \(30\) is an outlier. The full range is \(30-4=26\), even though the right whisker ends at \(20\).

Compare a typical value using the median and consistency using IQR or range, in the original context. A higher median and a smaller IQR describe different features. Approximate symmetry of the box and whiskers is consistent with a normal model, but a box plot alone cannot prove normality.

Write \(\operatorname{IQR}=Q_3-Q_1\). Flag observations strictly below \(Q_1-1.5\operatorname{IQR}\) or strictly above \(Q_3+1.5\operatorname{IQR}\). Equality with a fence is not flagged by this rule; investigate a flagged observation before removing it.