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High Quality Content by WIKIPEDIA articles! Quantiles are points taken at regular intervals from 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. More generally, one can consider the quantile function for any distribution. This is defined for real variables between zero and one and is mathematically the inverse of the cumulative distribution function.