# Median

*This article is about the median used in statistics. For other medians, check Median (disambiguation).*

A **median** is a measure of central tendency used frequently in statistics.

## Contents

## Mean, Median, Mode

https://youtu.be/TkZvMa30Juo?t=1504

## Median of a data set

The median of a finite set of real numbers is defined to be such that . This turns out to be when is odd. When is even, all points between and are medians. If we have to specify one median we conventionally take . (Here denotes the order statistic.) For example, the median of the set is 7.

## Median of a distribution

### Median of a discrete distribution

If is a discrete distribution, whose support is a subset of a countable set , with for all positive integers , the median of is any point lying between and where and . If for some , is defined to be the median of .

### Median of a continuous distribution

If is a continuous distribution, whose support is a subset of the real numbers, the median of is defined to be the such that . Clearly, if has a density , this is equivalent to saying .

## Problems

### Pre-introductory

Find the median of .

### Introductory

2000 AMC 12 Problems/Problem 14

2004 AMC 12A Problems/Problem 10

### Intermediate

### Olympiad

*This page is in need of some relevant examples or practice problems. Help us out by adding some. Thanks.*