House prices in a town: most around $200k, one mansion at $5 million. The mean says 'average house = $400k'. The median says '$200k'. The median is telling the truth.
The median is the middle value when the data is sorted. Half the values are below it, half above.
Income, house prices, response times, anything with a long tail — the median resists outliers in a way the mean can't.
How to find it
- Sort the values from smallest to largest.
- Odd count → the middle one.
- Even count → the average of the two middle ones.
Median of 8, 3, 9, 1, 4, 7?
Why is median income reported instead of mean income?
A few extremely high earners pull the mean way up, making it unrepresentative. The median — the income of the person 'in the middle' — describes a typical earner honestly.
You must sort first. The median of 5, 1, 9 is 5, not 1 — sort to 1, 5, 9 and take the middle. Don't just grab the middle of the unsorted list.
The median is a special case of a percentile — it's the 50th percentile. Quartiles (25th, 75th) extend the same idea.
- Median = middle value of the sorted data.
- Even count → average the two middle values.
- Resistant to outliers — the right choice for skewed data.