Box plots and statistical comparisons

A box-and-whisker plot shows the minimum, lower quartile, median, upper quartile and maximum. The box contains the middle half of the data.

For ungrouped data in this chapter, order the values and take the median of each half to find the quartiles. When there is an odd number of values, exclude the overall median from both halves.

Compare a measure of centre and a measure of spread, then interpret both in context. For example, a shorter median waiting time describes a shorter typical wait; a smaller interquartile range describes more consistent waits for the middle half.

The mean is affected by extreme values. The median may better describe a typical value when an isolated extreme value pulls the mean away from most observations. A box plot does not show every observation or the sample size.

Before accepting a statistical claim, check the population surveyed, how the sample was selected, the axis scale and whether the conclusion follows from the displayed data.