This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.

# Quantile

 Quantile[list, q]gives the qth quantile of list. Quantile[list, {q1, q2, ...}]gives a list of quantiles q1, q2, ... . Quantile[list, q, {{a, b}, {c, d}}]uses the quantile definition specified by parameters a, b, c, d. Quantile[dist, q]gives a quantile of the symbolic distribution dist.
• Quantile[{{x1, y1, ...}, {x2, y2, ...}, ...}, q] gives {Quantile[{x1, x2, ...}, q], Quantile[{y1, y2, ...}, 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+dFractionalPart[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}}.
• Common choices of parameters include:
• Quantile[list, q] always gives a result equal to an element of list.
• The same is true whenever d=0.
• When d=1, Quantile is piecewise linear as a function of q.
• 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.
Find the half-way value (median) of a list:
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Find the quarter-way value (lower quartile) of a list:
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Lower and upper quartiles:
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The qth quantile for a normal distribution:
 Out[1]=
 Scope   (6)
 Applications   (3)