---
tag: 58NHGZDSRE
kind: concept
name: Order statistic
msc: [62G30]
specializes: [0Q5CG2NEQ8]
sources:
  - url: https://en.wikipedia.org/wiki/Order_statistic
same_as:
  wikidata: Q1767128
  wikipedia: Order statistic
---

## Summary

The $k$-th order statistic of a sample is its $k$-th smallest value.
The minimum, the maximum, the median and the sample quantiles are order statistics or simple functions of them.
They are the basis of many nonparametric and robust methods, and their distributions have explicit formulas for i.i.d. samples.

## Explanations

### L1 human

Write the numbers of a sample in increasing order.
The first number in the sorted list is the first order statistic, the second is the second, and so on.
For the sample $5, 1, 3$, the sorted list is $1, 3, 5$, so the order statistics are $1$, $3$ and $5$.
The middle one, $3$, is the sample median.