Maths
What are the mean, median and mode?
Quick answer
Mean, median and mode are three kinds of average. The mean shares the total out equally, the median is the middle value in order, and the mode is the most common value.
In one sentence
Mean, median and mode are three different ways of finding a "typical" value in a set of numbers.
Explained
Five friends play a game and score 2, 3, 3, 6 and 11 goals over a season. What is a typical score? There are three good answers.
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Mean. Add all the values and divide by how many there are. 2 + 3 + 3 + 6 + 11 = 25, and there are 5 friends, so the mean is 25 ÷ 5 = 5. The mean imagines sharing the goals out equally. When people say "average" without saying which, they usually mean the mean.
Median. Put the values in order and pick the middle one. In 2, 3, 3, 6, 11 the middle value is 3. If there is an even number of values, the median is halfway between the two middle ones.
Mode. The value that appears most often. Here 3 appears twice, so the mode is 3. A set can have no mode (all different) or more than one mode. The mode is the only average that works for non-numbers too, like the most popular ice cream flavour.
A useful extra is the range: the biggest value minus the smallest, 11 − 2 = 9. It shows how spread out the data is.
Which average is best? The mean uses every value, but one extreme value pulls it a long way. Here, the 11 drags the mean up to 5, even though three of the five friends scored 3 or fewer. The median ignores extremes, which is why house prices and incomes are often reported as medians. The mode suits things you count or choose, like shoe sizes in a shop.
Examples
| Data | Mean | Median | Mode | Range |
|---|---|---|---|---|
| 5, 5, 6, 8, 11 | 35 ÷ 5 = 7 | 6 | 5 | 6 |
| 1, 2, 3, 4 | 10 ÷ 4 = 2.5 | 2.5 | none | 3 |
| 20, 22, 22, 25, 96 | 185 ÷ 5 = 37 | 22 | 22 | 76 |
In the last row, one big value (96) makes the mean bigger than four of the five numbers. The median, 22, describes the group better.
Common mistakes
- Finding the median without sorting. Always put the numbers in order first.
- Dividing by the wrong number for the mean. Count the values, including any zeros.
- Giving how many times the mode appears instead of the value itself. In 4, 4, 4, 7 the mode is 4, not 3.
Quick quiz
Mean, median and mode
Check what you know with 5 quick questions.
Question 1 of 5
What is the mean of 4, 6 and 11?
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Mean, median and mode practice
For grown-ups
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