Mean Calculator
The arithmetic mean of your numbers, with variance and standard deviation alongside it. Switch between sample and population with one click.
- Runs in your browser
- Sample or population
- Shows the working
- Free
Find the mean
Separate with spaces, commas or new lines. Paste a whole column straight from a spreadsheet.
Show the working
How the mean and standard deviation are calculated
Mean
Add every number and divide by the count. For 2, 4, 4, 4, 5, 5, 7, 9 the sum is 40 and there are 8 numbers, so the mean is 5.
Variance
Take each number minus the mean, square it, add them all up, then divide by n (population) or n − 1 (sample). Here: 32 ÷ 8 = 4, or 32 ÷ 7 ≈ 4.57.
Standard deviation
The square root of the variance. Population: √4 = 2. Sample: √4.57 ≈ 2.14. It says how spread out the numbers are, in the same units as the data.
Questions people ask
What is the mean of a set of numbers?
The arithmetic mean is the sum of the numbers divided by how many there are. It is what most people call the average.
Sample or population: which should I pick?
Pick population if your numbers are the entire group you care about (every student in one class). Pick sample if they are a subset standing in for a bigger group (100 customers out of thousands). Sample divides by n − 1, which makes the result slightly larger to account for the missing data.
What does standard deviation tell me?
How far the numbers typically sit from the mean, in the same units as the data. A small standard deviation means the values cluster tightly; a large one means they are spread out.
Is this the same as Excel STDEV?
Sample mode matches Excel STDEV and STDEV.S. Population mode matches STDEV.P.
What is the difference between mean and median?
The mean uses every value, so one very large number pulls it up. The median is just the middle value once sorted, so it ignores extremes. Median calculator →