Variance 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: 5, 7, 9, 11; Data is a: Sample (divide by n − 1) | The sample standard deviation is 2.581989 and the variance is 6.666667. |
How to use it
Variance is the average of the squared differences from the mean: add up (x − mean)² for every value, then divide by n for a population or n − 1 for a sample. It is the square of the standard deviation.
Because it is squared, variance is in squared units, which is why the standard deviation (its square root) is often easier to read.
Frequently asked questions
How do I calculate variance?
Find the mean, square each value's difference from it, add the squares, and divide by n (population) or n − 1 (sample).
What is the variance of 2, 4, 4, 4, 5, 5, 7, 9?
Population variance is 4; sample variance is about 4.5714.
How is variance related to standard deviation?
Standard deviation is the square root of the variance.
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.