Five-Number Summary vs Boxplot

Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.

Five-number summary

Describing data

The five-number summary reports a data set's minimum, first quartile, median, third quartile, and maximum.

The five-number summary captures the center and spread of a distribution with five ordered values: minimum, Q1Q_1 (the first quartile), median, Q3Q_3 (the third quartile), and maximum. For example, the summary 2, 5, 8, 12, 20 says the data run from 2 to 20 with a median of 8. These five numbers are exactly what a boxplot draws, and the gap Q3Q1Q_3 - Q_1 gives the interquartile range. Together they describe spread without assuming any particular distribution shape.

Full entry for five-number summary

Boxplot

Graphs and displays

A boxplot is a graph of the five-number summary, with a box from Q1 to Q3, a line at the median, and whiskers to the extremes.

A boxplot turns the five-number summary into a picture: a box spans Q1Q_1 (the first quartile) to Q3Q_3 (the third quartile), a line inside marks the median, and whiskers reach the smallest and largest non-outlier values. For example, a longer right whisker signals a right-skewed distribution. Points more than 1.5×IQR1.5 \times \text{IQR} beyond the nearer quartile are drawn separately as outliers. Boxplots make it easy to compare center and spread across several groups side by side.

Full entry for boxplot

Where each one fits in the course