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.