A median is the middle value of a set of numbers when they are arranged in order from smallest to largest.

Simple definition

  • Line up all the numbers in order.
  • If there is an odd number of values, the median is the one right in the middle.
  • If there is an even number of values, the median is the average of the two middle numbers.

Example (odd count):
Data: 1, 2, 3, 5, 6, 7, 12 → median is 5 (three numbers are smaller, three are larger).

Example (even count):
Data: 1, 2, 3, 4, 5, 9 → middle two are 3 and 4, so median = (3+4)/2=3.5(3+4)/2=3.5(3+4)/2=3.5.

Why the median matters

  • It is a measure of “central tendency” (a way to describe the center of the data), along with mean and mode.
  • It is less affected by extreme values (outliers) than the mean, so it often gives a better sense of a “typical” value when the data are skewed (like incomes or house prices).

How to find the median (step‑by‑step)

  1. Arrange the data in order from smallest to largest.
  1. Count how many values there are; call this number nnn.
  1. If nnn is odd: the median is the n+12\frac{n+1}{2}2n+1​-th value in the ordered list.
  1. If nnn is even: take the n2\frac{n}{2}2n​-th and (n2+1)\left(\frac{n}{2}+1\right)(2n​+1)-th values and average them.

Quick comparison with “average” (mean)

  • Mean : add all the numbers and divide by how many there are.
  • Median : take the middle value (or the average of the two middle values).
  • When a few values are very large or very small, the median can be a more representative center than the mean.

In everyday stats like “median income” or “median house price,” median is used so that a few very rich or very expensive cases do not distort the picture of what’s typical.

TL;DR: The median is the middle number in ordered data, or the average of the two middle numbers if there isn’t a single middle.