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Quantile

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

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

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

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

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

FilledSmallSquare 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.

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

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

FilledSmallSquare The same is true whenever .

FilledSmallSquare When , Quantile is piecewise linear as a function of .

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

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

FilledSmallSquare Quantile works with SparseArray objects.

FilledSmallSquare See Section 1.6.7, Section 3.2.14 and Section 3.8.1.

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

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

FilledSmallSquare New in Version 5.0.

Further Examples