Mean, median and mode: what's the difference?
"Average" usually means the mean, but there are three common types, and each one tells you something slightly different.
- Mean: add everything up and divide by how many there are. It uses every number, so one very big or very small value can pull it a long way.
- Median: put the numbers in order and take the middle one. If there's an even number of values, it's halfway between the two in the middle. One extreme value barely moves it.
- Mode: the number that comes up most often. There can be more than one mode, or none at all if every number is different.
The range isn't an average. It's the gap between the smallest and largest numbers, and shows how spread out the data is.
mean = total ÷ count
range = largest − smallest
Worked example
Take the numbers 4, 8, 15, 16, 23 and 42.
- Mean: 4 + 8 + 15 + 16 + 23 + 42 = 108. There are 6 numbers, so 108 ÷ 6 = 18.
- Median: they're already in order. With 6 numbers the middle two are 15 and 16, so the median is (15 + 16) ÷ 2 = 15.5.
- Mode: every number appears once, so there's no mode.
- Range: 42 − 4 = 38.
Notice the mean (18) is higher than the median (15.5). That's the 42 pulling it up, which is a sign the data is lopsided.
Why the median is often better
When a few values are much bigger than the rest, the median gives a fairer picture of what's "typical". That's why the Office for National Statistics reports median earnings and house prices. A handful of very high salaries or very expensive houses would push the mean up, so it wouldn't reflect what most people actually earn or pay.
For example, if five people earn £24,000, £27,000, £30,000, £32,000 and £250,000, the mean is £72,600, which none of them is anywhere near. The median is £30,000, which is much more representative.
What is standard deviation?
Standard deviation measures how spread out the numbers are around the mean. A small standard deviation means most numbers sit close to the average. A big one means they're widely scattered. For the example above, the population standard deviation is about 12.3.
Use the population figure when your numbers are the whole group, such as every pupil's mark in one class. Use the sample figure when your numbers are a sample taken from a bigger group, such as 50 people surveyed to represent a whole town. The sample version divides by one less than the count, which makes it slightly bigger to allow for the people you didn't ask.
Tips
- Don't put commas inside big numbers. Type 1500, not 1,500, or the calculator will read it as 1 and 500.
- Averaging percentages or rates? A simple mean can mislead when the groups are different sizes. Weight each one by its size, or add up the totals first.
- Need a percentage change instead? Use the percentage calculator.
- Averaging fuel use or running pace? The MPG calculator and running pace calculator handle those properly.
Frequently asked questions
How do I work out the mean average?
Add all the numbers together, then divide by how many numbers there are. For 2, 4 and 9 the total is 15, and 15 ÷ 3 = 5.
How do I find the median?
Put the numbers in order from smallest to largest and take the middle one. If there is an even number of values, the median is halfway between the two middle numbers.
What if there is no mode?
If every number appears the same number of times, there is no mode. If two or more numbers tie for most common, they are all modes.
What is the difference between mean and median?
The mean adds everything and divides by the count, so very high or low values pull it. The median is the middle value, so it isn't affected much by extremes.
Should I use population or sample standard deviation?
Use population when your numbers cover the whole group you are interested in. Use sample when your numbers are a sample from a bigger group.
Last reviewed October 2026. Results are rounded to 4 decimal places.