Mean, Median, Mode and Range
“Average” can mean three different things, and choosing the wrong one can be badly misleading. Learn all three, plus range, and when to use each.
~8 min3 lessonsInteractive calculator5-question quiz
01
The four numbers
| Measure | How to find it | For 2, 3, 3, 5, 12 |
|---|---|---|
| Mean | Add them up, divide by how many | 25 ÷ 5 = 5 |
| Median | Sort them; take the middle one | 2, 3, 3, 5, 12 |
| Mode | The value that appears most | 3 |
| Range | Biggest minus smallest | 12 − 2 = 10 |
Mean, median and mode are all kinds of “average”: a single number that sums up the middle of the data. Range tells you how spread out it is.
02
Medians with an even count
With an even number of values there's no single middle one. Take the two middle values and find the number halfway between them.
Example · 4, 7, 9, 10
- Already sorted; the middle two are 7 and 9
- (7 + 9) ÷ 2 = 8
- Median = 8
Don't forget to sort. The median of 9, 2, 7 is 7, not 2. Put the numbers in order first.
A list can have no mode (every value appears once) or several modes (a tie).
03
Which average should you trust?
The mean gets pulled around by extreme values; the median doesn't.
Example · salaries at a small company
- Nine people earn $50,000 and the owner earns $1,050,000
- Total pay is $1,500,000, so the mean is $1,500,000 ÷ 10 = $150,000
- Median = $50,000
- The median describes a typical employee far better
- Use the median for things with big outliers: house prices, incomes, waiting times.
- Use the mean when values are fairly even: test scores, temperatures, heights.
- Use the mode for categories: the most popular shoe size or flavour.
Try it · average calculator