Definition · Plain-language
Boxplot
A boxplot (box-and-whisker plot) is a chart that summarises a distribution through its five-number summary: minimum, first quartile, median, third quartile and maximum.
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The five-number summary
A boxplot is a visual display of the five-number summary, the five values that concisely describe a distribution. These are the minimum (smallest value), the first quartile or Q1 (the 25th percentile, below which a quarter of the data falls), the median or Q2 (the 50th percentile, the middle value), the third quartile or Q3 (the 75th percentile) and the maximum (largest value). Together these five points divide the ordered data into four parts, each containing roughly a quarter of the observations, giving a compact picture of centre, spread and shape without plotting every data point.
The box and the whiskers
The box stretches from Q1 to Q3 and therefore spans the interquartile range (IQR = Q3 − Q1), which contains the middle 50% of the data. The line drawn inside the box marks the median, not the mean. Two whiskers extend outward from the box towards the smaller and larger values. In the common convention, each whisker reaches to the most extreme data point lying within 1.5 × IQR of the nearer quartile; values beyond that limit are drawn as individual points and treated as potential outliers. Other conventions extend the whiskers all the way to the minimum and maximum, so always check which is in use.
How to read shape and spread
A boxplot reveals a distribution’s spread and symmetry at a glance. A wider box or longer whiskers mean greater variability. The position of the median line within the box signals skew: a median nearer Q1 (with a longer upper whisker) suggests positive, right skew, while a median nearer Q3 suggests negative, left skew. A roughly central median with similar whiskers suggests symmetry. Because boxplots are based on quartiles rather than the mean, they are resistant to extreme values, which makes them well suited to comparing several groups side by side and to spotting differences in centre and spread quickly.
Key facts
At a glance
- Definition: a chart of the five-number summary of a dataset
- Also called: box-and-whisker plot
- Five numbers: minimum, Q1, median, Q3, maximum
- Box: spans Q1 to Q3, i.e. the interquartile range (middle 50%)
- Median line: the line inside the box marks the median, not the mean
- Outliers: points beyond 1.5 × IQR of the quartiles are plotted separately
Common misconceptions
What people often get wrong
Often heard: The line inside the box of a boxplot shows the mean of the data.
Actually: It marks the median (the middle value), not the mean. Boxplots are built entirely from quartiles, which is what makes them resistant to extreme values.
Often heard: Each of the four sections of a boxplot covers an equal width of data values.
Actually: Each section contains about a quarter of the data points, not an equal range of values. A short section means values are densely packed; a long one means they are spread out.
Often heard: The whiskers of a boxplot always reach to the true minimum and maximum.
Actually: Under the common 1.5 × IQR convention, whiskers stop at the furthest point within that limit, and anything beyond is plotted as an outlier. Whisker rules vary, so check the convention.
