quantile

A quantile is a set of values which partitions a probability distribution into subsets of equal size.

Formally,
given a random variable $X$ with cumulative distribution function $F(x)$,
the $k^{th}$ $q$-quantile is the value $x$ such that

i.e. the distribution is divided into $q$ subsets of equal size, and $k\in [1,(q-1)]$.

This definition can be expanded to the $p$-quantile $x_p$ with $p\in [0,1]\subseteq \mathbb{R}$ such that $p=\frac{k}{q}$.

There is only one 2-quantile, the median.

The difference between the upper and lower 4-quantiles (quartiles) is the interquartile range.

The 100-quantiles are called percentiles.