Modified boxplot

A modified boxplot plots outliers as separate points and draws each whisker only to the most extreme value still inside the IQR fences.

A modified boxplot is the version you normally draw, because it shows outliers instead of burying them at the end of a long whisker. You first set the fences at Q11.5×IQRQ_1 - 1.5 \times \text{IQR} and Q3+1.5×IQRQ_3 + 1.5 \times \text{IQR}, where Q1Q_1 is the first quartile and Q3Q_3 is the third quartile, taking both by the median-excluded (TI-84) rule this site uses, then mark every value beyond a fence with its own dot. Suppose Q1=20Q_1 = 20 and Q3=32Q_3 = 32, so the IQR is 12 and the fences sit at 2018=220 - 18 = 2 and 32+18=5032 + 18 = 50: a value of 61 becomes a plotted point, and the upper whisker stops at the largest value at or below 50. The box is unchanged either way, still running from Q1Q_1 to Q3Q_3 with the median marked inside it.

Where this comes up

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