# Quantile

(Redirected from quantile)
• Quantiles are values taken at regular intervals from the inverse of the cumulative distribution function (CDF) of a random variable. Dividing ordered data into $q$ essentially equal-sized data subsets is the motivation for $q$-quantiles; the quantiles are the data values marking the boundaries between consecutive subsets. Put another way, a $k^\mathrm{th}$ $q$-quantile for a random variable is a value $x$ such that the probability that the random variable will be less than $x$ is at most $k/q$ and the probability that the random variable will be greater than $x$ is at most $(q-k)/q=1-(k/q)$. There are $q-1$ of the $q$-quantiles, one for each integer $k$ satisfying $0 \lt k \lt q$. In some cases the value of a quantile may not be uniquely determined, as can be the case for the median of a uniform probability distribution on a set of even size.