# Quantile

## Statistical method of dividing data into equal-sized intervals for analysis / From Wikipedia, the free encyclopedia

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In statistics and probability, **quantiles** are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities, or dividing the observations in a sample in the same way. There is one fewer quantile than the number of groups created. Common quantiles have special names, such as *quartiles* (four groups), *deciles* (ten groups), and *percentiles* (100 groups). The groups created are termed halves, thirds, quarters, etc., though sometimes the terms for the quantile are used for the groups created, rather than for the cut points.

**q**-**quantiles** are values that partition a finite set of values into q subsets of (nearly) equal sizes. There are *q* − 1 partitions of the q-quantiles, one for each integer k satisfying 0 < *k* < *q*. In some cases the value of a quantile may not be uniquely determined, as can be the case for the median (2-quantile) of a uniform probability distribution on a set of even size. Quantiles can also be applied to continuous distributions, providing a way to generalize rank statistics to continuous variables (see percentile rank). When the cumulative distribution function of a random variable is known, the q-quantiles are the application of the* quantile function* (the inverse function of the cumulative distribution function) to the values {1/*q*, 2/*q*, …, (*q* − 1)/*q*}.