The median is the value in the middle of the data once it is sorted from smallest to largest. Half the values lie below it, half above. It answers a different question from the mean: not "what is the fair share?" but "what is the typical value in the middle of the pack?"

Odd and even counts

• With an odd number of values, the median is the single one in the middle. For 3, 4, 5, 7, 9 the median is 5.
• With an even number, there are two middle values — the median is their average. For 2, 4, 6, 8 it is (4+6)/2 = 5.

The median's superpower is that it is robust: because it only cares about the middle position, a wild outlier at one end barely moves it. The mean, where every value votes, is dragged along instead.

Median versus mean under an outlier

Drag the orange point toward an extreme. Two lines track the data: the mean chases the outlier, while the median barely flinches — it stays anchored at the middle of the sorted values. This is exactly why incomes and house prices are usually reported as medians.