Variance Calculator
Calculate population and sample variance for a data set.
What the Variance Calculator does
Variance measures how far values sit from the mean, averaged over squared distances. Squaring stops positive and negative deviations from cancelling, but it also means variance is expressed in squared units — which is why the standard deviation is usually quoted instead.
Formula
Population: σ² = Σ(x − μ)² ÷ nSample: s² = Σ(x − x̄)² ÷ (n − 1)
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Numbers | text | Yes | Separate values with commas, spaces or new lines. |
| Data set type | one of 2 options | Yes | — |
How to use it
- Choose Data set type.
- Enter Numbers.
- Select Calculate.
Worked example
Sample measurements of 4, 8, 6, 5 and 3.
- Numbers
- 4, 8, 6, 5, 3
- Type
- Sample
Mean 5.2, squared deviations sum to 14.8, so s² = 14.8 ÷ 4 = 3.7.
Frequently asked questions
Why divide by n − 1 for a sample?
Because the sample mean sits closer to your data than the true population mean does, which understates spread. Dividing by n − 1 — Bessel's correction — removes that bias.