Boxplots and spread comparisons

A boxplot summarises five positions

A boxplot marks the minimum, Q1, median, Q3 and maximum under the stated convention. The box length is the IQR, while the full whisker span is the range when whiskers use the minimum and maximum. A task using an outlier convention must state it; do not assume that every whisker is automatically a maximum.

For summaries 2, 5, 7, 11, 18, draw a box from 5 to 11, a median line at 7 and whiskers to 2 and 18 on one numerical axis. The IQR is 6 and the range 16. The drawing does not reveal individual observations inside those regions.

Compare only what is shown

Two boxplots have the same median but different IQRs. You can compare their central position and middle-half spread. You cannot determine exact means or exact counts above every threshold from the five-number summaries alone.

Check your understanding 1 Compare the box with the whole span

A boxplot has minimum 2, Q1 5, median 7, Q3 11 and maximum 18. Find its range and interquartile range.

Your answer or drawing on paper

Show answer

The range is 18 − 2 = 16; IQR is 11 − 5 = 6. The box shows the middle-half spread, while the full span uses the two extremes. Neither summary determines every observation.