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In statistics, the nth order statistic of a sample is equal to the nth-smallest sample value.

For example, if the sample values are:

6, 9, 3, 8

then the second order statistic is:

x(2) = 6.

The first order statistic (or smallest order statistic) is always the minimum of the sample. For a sample of size n, the nth order statistic (or largest order statistic) is the maximum.

In conventional notation, one writes:

x1 = 6
x2 = 9
x3 = 3
x4 = 8

with no round brackets () in the subscripts, referring to the data in the order in which they appear, and:

x(1) = 3
x(2) = 6
x(3) = 8
x(4) = 9

with round brackets () in the subscripts, referring to the order statistics, i.e., the data sorted into increasing order.

Contrast with quantiles....

See also



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Topics: Order Statistic, Ordered Pair, Order Automorphism, Ordered Field...

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