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 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.

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.

Statistics

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Box Plots, Outliers and Comparing Distributions

Box Plots, Outliers and Comparing Distributions