Quartile

A quartile is one of three cut points that divide a sorted dataset into four equal-sized parts, describing how the values are spread out.

Where the median tells you the centre of a dataset, quartiles tell you about its spread. Sort the values and split them into four equal groups, and the three boundaries between those groups are the quartiles. They give a quick sense of where the bulk of the data sits and how stretched it is, without listing every value.

The three quartiles

The first quartile (Q1), at the 25th percentile, is the value below which a quarter of the data falls. The second quartile (Q2), at the 50th percentile, is the median itself. The third quartile (Q3), at the 75th percentile, is the value below which three-quarters of the data falls. The distance from Q1 to Q3 is the interquartile range (IQR) — the span of the middle half of the data, a measure of spread that ignores the extremes.

A concrete example

Take eight values sorted in order: 2, 4, 5, 7, 8, 10, 12, 20. The median (Q2) sits between 7 and 8, so 7.5. The lower half is 2, 4, 5, 7, whose middle gives Q1 = 4.5; the upper half is 8, 10, 12, 20, giving Q3 = 11. The interquartile range is 11 − 4.5 = 6.5, meaning the central half of the values spans about 6.5 units — a compact summary of where most of the data lives.

How quartiles appear in a chart

Quartiles are the skeleton of a box plot: the box stretches from Q1 to Q3, with the median drawn as a line inside it, so the box itself depicts the interquartile range. This makes the spread of a distribution visible at a glance and is a standard way to compare several groups side by side.

Related terms

The middle quartile is the median, and points lying far beyond Q1 or Q3 are often flagged as outliers. Quartiles summarise the kind of distribution you can also see in full in the histogram guide.