Average Calculator

“Average” means more than one thing

Usually it means the mean: add everything up, divide by how many there are. But the median — the middle value when sorted — is often the more honest description, and the two can be very far apart.

mean = sum ÷ count     median = the middle value

Why they disagree

The numbers loaded above are 12, 15, 11, 14, 62, 13, 12. The mean is 19.9. The median is 13. Six of the seven numbers are below the mean.

One large value has dragged the mean upwards, and the mean is now a poor description of a typical number in the set. The median is unaffected, because it only cares about position, not size.

This is exactly why incomes are reported as medians. A handful of very high earners pull the mean above what most people actually earn, so the mean income describes almost nobody.

What the other figures tell you

• Range — largest minus smallest. A quick measure of spread, but one outlier defines it entirely.
• Standard deviation — roughly, how far a typical value sits from the mean. Small means tightly clustered; large means spread out. It uses every value, so it is more robust than the range.

The standard deviation here is the population one, which treats your numbers as the whole group. If they are a sample drawn from something larger, the sample standard deviation divides by one less and comes out slightly higher.

A rule of thumb

If the mean and the median are close, the data is fairly symmetrical and the mean is a fine summary. If they are far apart, something is skewing the distribution, and the median usually describes the group better.

Common uses

• Marks and grades across a set of results.
• Times, weights or measurements taken repeatedly.
• Prices gathered from several suppliers.
• Checking a claimed average by asking whether it is the mean or the median, and what the spread looks like.

The working, step by step

Questions people ask

What is the difference between mean and median?

The mean is the total divided by the count. The median is the middle value once sorted. One extreme value moves the mean a long way and the median barely at all.

Which average should I use?

If the mean and median are close, either. If they are far apart, the median usually describes the group better.

Why are incomes reported as medians?

Because a small number of very high earners pull the mean above what most people earn, so the mean describes almost nobody.

What does standard deviation tell me?

Roughly how far a typical value sits from the mean. Small means tightly clustered, large means spread out.

How should I separate my numbers?

Spaces, commas, semicolons or new lines all work.

Nothing here is sent anywhere

The arithmetic happens in your browser as you type. The numbers you enter are not transmitted, logged or stored, because the page has no server behind it to receive them.