# Quartile

From AMS Glossary

## 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 Thus,

*Q*_{1},*Q*_{2},*Q*_{3}and are defined in terms of the distribution function*F*(*x*) as follows:*Q*_{2}coincides with the median. In empirical relative frequency tables, the quartiles are estimated by interpolation. The interquartile range 2*Q*is the distance from*Q*_{1}to*Q*_{3}; 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.