Box-and-Whisker Plots

To understand box-and-whisker plots, you have to understand medians and quartiles of a data set.

The median is the middle number of a set of data, or the average of the two middle numbers (if there are an even number of data points).

The median (Q2) divides the data set into two parts, the upper set and the lower set. The lower quartile (Q1) is the median of the lower half, and the upper quartile (Q3) is the median of the upper half.

Example:

Find Q1, Q2, and Q3 for the following data set:

2, 6, 7, 8, 8, 11, 12, 13, 14, 15, 22, 23

There are 12 data points. The middle two are 11 and 12. So the median, Q2, is 11.5.

The "lower half" of the data set is the set {2, 6, 7, 8, 8, 11}. The median here is 7.5. So Q1 = 7.5.

The "upper half" of the data set is the set {12, 13, 14, 15, 22, 23}. The median here is 14.5. So Q3 = 14.5.

A box-and-whisker plot displays the values Q1, Q2, and Q3, along with the extreme values of the data set (2 and 23, in this case):

A box & whisker plot shows a "box" with left edge at Q1, right edge at Q3, the "middle" of the box at Q2 (the median) and the maximum and minimum as "whiskers".