Three kinds of average
- Mean — add everything up and divide by how many. The usual "average", and the one a single extreme value can drag away from the truth.
- Median — the middle value when they are lined up in order. Unmoved by extremes, which is why incomes and house prices are reported this way.
- Mode — the value that appears most often. The only average that works for things you cannot add, like shoe sizes or survey answers.
Formula
Mean = sum ÷ countVariance = Σ(x − mean)² ÷ nfor a whole population, or÷ (n − 1)for a sampleStandard deviation = √variance
Worked example
For 12, 15, 11, 19, 15, 14, 22, 15, 9, 18: the mean is 15, the median is 15, and 15 is also the mode, appearing three times. The range runs from 9 to 22 and the standard deviation is about 3.6 — most values sit within about 3.6 of the mean.
How to use the calculator
- Paste the numbers in any format — commas, spaces, new lines or a column copied from a spreadsheet.
- Read the mean first, then compare it with the median. A big gap means something is pulling the mean.
- Tick "sample" if your numbers are a sample of a larger group rather than the whole group.
Reading the spread
- A small standard deviation means the values huddle near the mean; a large one means they are scattered.
- For roughly bell-shaped data, about two thirds of values fall within one standard deviation of the mean.
- Always look at the smallest and largest value. One typo of an extra zero shows up there immediately.
Frequently asked questions
What is the difference between mean and median?
The mean adds everything and divides; the median is the middle value in order. When a few very large or very small numbers are present, the median describes the typical case better.
When should I use n − 1?
When your numbers are a sample taken from a bigger population and you want to estimate that population’s spread. For the whole group, divide by n.
Can a list have more than one mode?
Yes. If several values tie for the most appearances, they are all modes — the calculator lists them all.