Box Plots

The five-number summary as a picture

A box plot (also called a box-and-whisker plot) draws five numbers on a single scale: the minimum, the lower quartile (Q_1), the median (Q_2), the upper quartile (Q_3) and the maximum.

The box stretches from Q_1 to Q_3, so its width is the interquartile range. A line drawn inside the box marks the median, and the two whiskers reach out to the smallest and largest values.

At a glance the box shows where the central half of the data sits, while the whiskers show how far the tails stretch.

Reading a box plot

For a data set with five-number summary min, Q_1, median, Q_3, max:

the box runs from Q_1 to Q_3, with the median marked by a line inside it;
the box's width is the interquartile range, \text{IQR} = Q_3 - Q_1;
the whiskers reach out to the two extremes — the minimum and the maximum;
the full range is \text{max} - \text{min};
box plots make it easy to compare two data sets' spread and average side by side.