Standard deviation calculator
Calculator
The calculator needs JavaScript. The tables below give the same numbers for common cases.
How it is worked out
- Mean = 40 ÷ 8 = 5.
- Add the squared differences from the mean: 32.
- Divide by n − 1 = 7: variance = 4.571429.
- Standard deviation = √4.571429 = 2.13809.
| Inputs | Answer |
|---|---|
| Numbers: 2,4,4,4,5,5,7,9; Data is a: Whole population (divide by n) | The population standard deviation is 2 and the variance is 4. |
| Numbers: 2,4,4,4,5,5,7,9; Data is a: Sample (divide by n − 1) | The sample standard deviation is 2.13809 and the variance is 4.571429. |
| Numbers: 10, 12, 23, 23, 16, 23, 21, 16; Data is a: Sample (divide by n − 1) | The sample standard deviation is 5.237229 and the variance is 27.428571. |
How to use it
Standard deviation measures how spread out numbers are around their mean. Find the mean, square each difference from it, add them up, divide by n for a whole population or by n − 1 for a sample, then take the square root.
Use the sample version when your numbers are a sample drawn from a larger group (the usual case); use the population version when your numbers are the whole group. The variance, the square of the standard deviation, is shown too.
Frequently asked questions
What is the difference between sample and population standard deviation?
The sample version divides by n − 1 to correct for estimating the mean from the data; the population version divides by n.
What is the standard deviation of 2, 4, 4, 4, 5, 5, 7, 9?
The population standard deviation is 2; the sample standard deviation is about 2.138.
What does a large standard deviation mean?
The numbers are spread far from the mean; a small one means they cluster close to it.
Method: standard arithmetic shown step by step; no outside data is used. Checked 2026-11-12.
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General information only. Results are plain arithmetic on the numbers you enter; check anything important (money, health, school work) against your own records or the official source.