Average calculator
Paste your numbers and get the mean, median, mode, range and standard deviation. Commas, spaces or new lines all work.
Three different averages, and why it matters which
"Average" is not one thing. There are three, they answer different questions, and picking the wrong one is how statistics end up misleading people.
- Mean. Add everything up, divide by how many. The one people usually mean by "average".
- Median. Line the numbers up in order and take the middle one. Half the values sit above it, half below.
- Mode. The value that turns up most often. A list can have two modes, or none at all.
Why the difference bites. Take five salaries: £24k, £26k, £28k, £30k and £400k. The mean is £101,600, which describes nobody in the room. The median is £28,000, which describes the middle person exactly. One big value drags the mean; the median shrugs it off. This is why pay and house prices are almost always reported as medians.
When to use which
Use the mean when the values are reasonably tight and you want the total shared out: average marks, average temperature, average delivery time.
Use the median when there are outliers, or when the data is skewed. Money almost always is: a few very large numbers stretch the top end and nothing balances them at the bottom, because you cannot earn less than nothing.
Use the mode for things you count rather than measure. The most common shoe size, the most common answer, the most common number of bedrooms. The mean number of bedrooms being 2.4 helps nobody.
Range and standard deviation
Range is simply the largest minus the smallest. It tells you how spread out the numbers are, in one blunt figure, and one freak value can blow it up.
Standard deviation is a steadier measure of spread: roughly, how far a typical value sits from the mean. A small standard deviation means the numbers huddle around the average; a large one means they scatter. This tool gives the population standard deviation, meaning it describes the numbers you actually pasted rather than estimating a wider population from a sample.
Pasting from a spreadsheet
Paste a column straight from Excel, Sheets or Numbers and it will work: new lines, tabs, commas and spaces are all treated as separators. Negatives and decimals are fine. Anything that is not a number is ignored rather than breaking the sum, so a stray heading will not stop it.
Common questions
How do I calculate the average?
Add all the numbers together and divide by how many there are. That gives the mean. Paste your numbers above and it does it for you, along with the median and mode.
What is the difference between mean, median and mode?
The mean is the total divided by the count. The median is the middle value when they are lined up in order. The mode is the value that appears most often. They can be very different numbers for the same list, and which one is honest depends on the data.
Which average should I use?
The mean for tightly grouped data, the median when there are outliers or the data is skewed (money almost always is), and the mode for things you count rather than measure. Five salaries averaging £101,600 because one person earns £400k tells you nothing useful; the median of £28,000 does.
Can a list have more than one mode?
Yes. If two or more values tie for most common, they are all modes. If every value appears exactly once there is no mode at all, and this calculator says so rather than picking one at random.
What is the median of an even number of values?
The midpoint of the two middle values. With four numbers you take the second and third, add them and halve. That means the median often is not a number that appears in your list.
Can I paste numbers from Excel?
Yes. Paste a column or a row and it will read it. New lines, tabs, commas and spaces all work as separators, and anything that is not a number is ignored.