Boxplots

Description

A box plot (box-and-whisker diagram) displays the spread and centre of a dataset using five key values:

• Minimum value
• Lower quartile (Q1)
• Median (Q2)
• Upper quartile (Q3)
• Maximum value

The box spans from Q1 to Q3 (the interquartile range), with a vertical line at the median. Whiskers extend from the box to the minimum and maximum.

$$\text{IQR} = Q3 - Q1$$

Box plots are useful for comparing two distributions — draw them on the same scale and comment on medians (centre) and IQRs (spread).

Reading a box plot: the wider the box, the more spread out the middle 50% of data.

Common error: marking the median at the midpoint of the box rather than reading its actual value. Also: confusing the range with the IQR — the range uses min and max, not Q1 and Q3.

Links

Median Interquartile range Cumulative frequency