Mean, median and mode explained with examples

When someone says the average salary is £35,000 or the average house costs £290,000, they are using one of three different ideas of average, and they rarely tell you which. The mean, the median and the mode can give very different answers for the same data, and choosing the wrong one can make a figure look more typical than it is. This guide shows how to work out each average by hand, with a small data set you can follow, explains why the mean can be misleading, and gives clear advice on which to use for pay, test scores, shoe sizes and more.

By Valtrinity. Updated 18 October 2026.

The mean: add up and divide

The mean is the one most people mean by average. Add all the values together and divide by how many there are. If five friends pay £4, £6, £6, £8 and £11 for lunch, the total is £35 and the mean is £35 divided by 5, which is £7.

The mean uses every value, which is its strength and its weakness. It is the balance point of the data, so it responds to every change. If one person pays £50 instead of £11, the total becomes £74 and the mean becomes £14.80, even though four out of five people spent less than £9.

The mean is the right choice when the values are fairly evenly spread, with no extreme values, and when you want a figure that can be used in further calculation, such as working out a total from an average. For example, if the mean daily sales are £420, then in a 30-day month the expected total is £12,600.

The median: the middle value

The median is the middle value when the data is put in order from smallest to largest. If there is an odd number of values, it is the one in the middle. If there is an even number, it is the mean of the two middle values.

Take the lunch prices again: £4, £6, £6, £8, £11. They are already in order, there are five of them, and the middle one is the third, which is £6. Now take six values: 3, 5, 8, 10, 12, 20. The two middle values are 8 and 10, and the median is 9.

The median is not affected by extreme values. With the £50 lunch the data becomes £4, £6, £6, £8, £50, and the median is still £6. That makes it a better description of a typical case when the data has a few very large or very small values. It is the reason the Office for National Statistics reports median earnings, not mean earnings, in its headline pay figures.

The mode: the most common value

The mode is the value that appears most often. In the data 6, 7, 7, 8, 8, 8, 9, the mode is 8, because it appears three times. A data set can have more than one mode if two values tie, and it can have none if every value appears once.

The mode is the only average that makes sense for categories rather than numbers. If you survey 50 people on their favourite fruit, you cannot add up apples and bananas to get a mean, but you can say that the most common answer, the mode, was apples. A shop that stocks shoes cares about the modal size for the same reason.

For numbers, the mode is most useful when the data is whole numbers with lots of repeats, such as shoe sizes, the number of people in a household, or the number of goals in a match. For measurements with many decimal places, repeated values are rare and the mode tells you little.

Why the mean can mislead: the salary example

Suppose a small firm has five employees earning £22,000, £24,000, £25,000, £27,000 and £120,000. The total is £218,000, so the mean salary is £43,600. The median is the middle value, which is £25,000. The mode does not exist, because each salary appears once.

Which is typical? Four out of five employees earn less than £28,000, so a mean of £43,600 describes nobody. The median of £25,000 is much closer to what most of the staff earn. This is a small version of what happens to national income data, where a minority of very high earners pull the mean upward.

The gap between the mean and the median is itself a clue. When the mean is well above the median, the data is skewed to the high end. When they are close, the data is roughly balanced. Anyone reading an average in a report should ask which one it is and, if possible, look at both.

A full worked example with test scores

A class of eleven pupils scores the following in a test out of 20: 8, 11, 12, 12, 13, 14, 14, 14, 16, 17, 19. Add them up: 8 plus 11 is 19, plus 12 is 31, plus 12 is 43, plus 13 is 56, plus 14 is 70, plus 14 is 84, plus 14 is 98, plus 16 is 114, plus 17 is 131, plus 19 is 150. The mean is 150 divided by 11, which is 13.64.

The data is already in order, and there are eleven values, so the median is the sixth. Counting along: 8, 11, 12, 12, 13, then 14. The median is 14. The mode is 14 as well, because it appears three times, more than any other score.

The three averages agree roughly here, with 13.6, 14 and 14, which suggests that the scores are fairly balanced. The low score of 8 pulls the mean down a little. Without it, the mean of the other ten pupils would be 142 divided by 10, which is 14.2.

Choosing the right average

For money, such as pay, house prices and spending, use the median as the headline figure, and mention the mean if you need it for totals. For test scores and similar data with no large outliers, the mean is usually fine. For categories, or for the most popular size, colour or option, use the mode.

If you have a lot of data, summarise it with two or three numbers. The mean and median together show whether the data is skewed. The range, which is the highest minus the lowest, shows how spread out it is. For a fuller picture of the spread, use the standard deviation.

One more tip: when you compare groups, use the same average for each. Comparing the mean of one group with the median of another is a common way to produce a misleading result.

Other types of mean

There are other means for special cases. The weighted mean gives some values more influence than others, as with a course mark where coursework counts for 40 per cent and an exam for 60 per cent. If you get 70 in coursework and 55 in the exam, the weighted mean is 0.4 times 70 plus 0.6 times 55, which is 28 plus 33, so 61.

The geometric mean is used for growth rates. If an investment grows by 10 per cent in one year and 20 per cent in the next, the average yearly growth is not 15 per cent. Multiply 1.10 by 1.20 to get 1.32, and take the square root, which is 1.149. The average yearly growth is 14.9 per cent.

For ordinary data, the simple mean, median and mode are all you need. The point is to know which one you are being shown.

Tools mentioned in this guide

Frequently asked questions