Quantile

Quantile[list, q] gives the q quantile of list.

Quantile[list, , , ... ] gives a list of quantiles , , ... .

Quantile[list, q, a, b, c, d] uses the quantile definition specified by parameters a, b, c, d.

Quantile[list, q] gives Sort[list, Less][[Ceiling[q Length[list]]]].

Quantile[, , ... , , , ... , ... , q] gives Quantile[, , ... , q], Quantile[, , ... , q].

For a list of length n, Quantile[list, q, a, b, c, d] depends on x = a + (n + b) q. If x is an integer, the result is s[[x]], where s = Sort[list, Less]. Otherwise the result is s[[Floor[x]]] + (s[[Ceiling[x]]] - s[[Floor[x]]]) (c + d FractionalPart[x]), with the indices taken to be 1 or n if they are out of range.

The default choice of parameters is {{0, 0}, {1, 0}}.

Quantile[list, q] always gives a result equal to an element of list.

The same is true whenever .

When , Quantile is piecewise linear as a function of .

Median[list] is equivalent to Quantile[list, 1/2, 1/2, 0, 0, 1].

About ten different choices of parameters are in use in statistical work.

Quantile works with SparseArray objects.

See Section 1.6.7, Section 3.2.14 and Section 3.8.1.

See also: Median, Ordering, Variance, Sort, ListInterpolation.

Related packages: Statistics`DescriptiveStatistics`, Statistics`MultiDescriptiveStatistics`.

New in Version 5.0.

Further Examples