How to use the Standard Deviation Calculator
- Paste your data set.
- Choose Sample if your data is a sample from a bigger group, or Population if it's the whole group.
- Read the standard deviation, variance and steps.
What does this tool do?
Standard deviation measures how far values typically sit from the mean. A small value means the numbers are clustered together; a large one means they're spread out.
Sample standard deviation divides by n − 1 instead of n (Bessel's correction). This corrects for the fact that a sample tends to underestimate the spread of the whole population.
Why use it?
- Shows both sample and population values side by side.
- Each step is shown, which is useful for statistics homework.
- Accepts data straight from a spreadsheet.
Example
For 4, 8, 6, 5, 3, 7 the mean is 5.5. The squared differences add up to 17.5. As a sample: 17.5 ÷ 5 = 3.5, so s = √3.5 ≈ 1.871. As a population: 17.5 ÷ 6 ≈ 2.917, so σ ≈ 1.708.
The formula
Privacy
The calculation happens instantly in your browser. The numbers you enter are not sent to our servers or saved. There's no account to create and nothing to install.
Frequently asked questions
Should I use sample or population?
If you measured every member of the group (every student in one class), use population. If your data stands in for a bigger group (100 customers out of thousands), use sample.
Last reviewed by the M2Toolkit team.