Quartile

quartile

One of a set of numbers (a quantile) on the random-variable axis that divides a probability distribution into four equal areas.

The three quartile points that lie between the extremes of the distribution are designated as Q₁, Q₂, Q₃ and are defined in terms of the distribution function F(x) as follows:

Thus, Q₂ coincides with the median. In empirical relative frequency tables, the quartiles are estimated by interpolation. The interquartile range 2Q is the distance from Q₁ to Q₃; half of this distance Q is called the semi-interquartile range (or quartile deviation) and is sometimes used as a crude measure of variability or spread.

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