Box plot

A box plot displays a dataset's median, quartiles and potential outliers through a box and extending whiskers. It compactly summarises distribution shape, spread and skewness and allows straightforward comparison of multiple groups.

ByHoang TruongUpdated July 2, 2026

See it move

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A box plot condenses a distribution to five figures. For one region's sales in thousands of euros, the minimum is 22, Q1 is 38, the median is 50, Q3 is 64, and the maximum is 82. The box spans Q1 to Q3 — an interquartile range of 26 — with whiskers reaching the min and max, both within 1.5 times the IQR of the box.

Where it fits

TopicDescriptive StatisticsCoreSubjectData Analysis & StatisticsCore

The formula

LaTeX

\text{Lower whisker bound} = Q_1 - 1.5 \times \text{IQR} \quad \text{Upper whisker bound} = Q_3 + 1.5 \times \text{IQR} \quad \text{IQR} = Q_3 - Q_1

Variables

$Q 1$: Lower quartile (25th percentile)
$Q 3$: Upper quartile (75th percentile)
$I QR$: Interquartile range: Q3 minus Q1

Observations beyond the whisker bounds are flagged as potential outliers and plotted as individual points.

Check yourself

PracticeCORE

A box plot displays Q1 = 40, median = 55, Q3 = 70. The whiskers extend to 10 and 90 using the 1.5 × IQR rule. A single dot appears at 100. What does the dot at 100 indicate?

Select an answer to check your understanding.