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 (Q_{2}) divides the data set into two parts, the upper set and the lower set. The **lower quartile **(Q_{1}) is the median of the lower half, and the **upper quartile **(Q_{3}) is the median of the upper half.

**Example:**

Find Q_{1}, Q_{2}, and Q_{3} 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, Q_{2}, 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 Q_{1} = 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 Q_{3} = 14.5.

A box-and-whisker plot displays the values Q_{1}, Q_{2}, and Q_{3}, 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 Q_{1}, right edge at Q_{3}, the "middle" of the box at Q_{2} (the median) and the maximum and minimum as "whiskers".