Mean, median or mode: which average should you use?
"Average" sounds like one thing, but statisticians use it for three different measures. Picking the wrong one can make a set of numbers look very different from what it really is.
The mean: share it out evenly
Add all the values and divide by how many there are. If five friends have 4, 6, 8, 10 and 12 sweets, the total is 40 and the mean is 8. It is what each person would get if everything were shared equally. It uses every value, which is its strength and its weakness.
The median: the middle one
Put the values in order and pick the middle. With 4, 6, 8, 10, 12 the median is 8. With an even number of values, take the halfway point of the middle two: for 4, 6, 8, 10 the median is 7.
The mode: the most common
The value that appears most often. For shoe sizes 6, 7, 7, 7, 8, 9 the mode is 7. It is the only one of the three that works for non-numerical data, like the most popular colour.
When outliers change the story
Imagine five salaries: $30k, $32k, $34k, $36k and $400k. The mean is $106,400, but nobody earns anything like that. The median, $34k, describes the typical person far better. This is why news reports on house prices and incomes nearly always use the median.
| Data | Mean | Median | Better choice |
|---|---|---|---|
| Test scores: 60, 62, 65, 68, 70 | 65 | 65 | Either: no outliers |
| Salaries with one huge value | Inflated | Typical | Median |
| Favourite subject votes | Not possible | Not possible | Mode |
| Daily temperature readings | Good | Good | Mean |
Range and spread
An average alone does not tell you how varied the data is. Two classes can both have a mean test score of 65, but one has everyone between 60 and 70 while the other ranges from 30 to 100. The range (largest minus smallest) gives a quick sense of the gap, and standard deviation gives a more complete picture.
A quick rule of thumb
- No extreme values and numbers you can add: use the mean.
- Skewed data or a few extreme values: use the median.
- Categories or "most popular": use the mode.
Try it yourself by pasting a list into the mean, median and mode calculator, then add one very large number and watch how the mean moves while the median barely does.
Paste your own list into the averages calculator.