Variance Calculator
Find the variance of a data set, sample or population, with every squared deviation shown.
About the Variance Calculator
Variance is the average squared distance from the mean. Squaring makes every deviation positive and weights large ones more. It's in squared units, so the standard deviation (its square root) is easier to interpret.
The formula
s² = Σ(x − x̄)² ÷ (n − 1), σ² = Σ(x − μ)² ÷ N
- n − 1
- sample: Bessel's correction for estimating from a sample
- N
- population: every member is included
Worked example
2, 4, 4, 4, 5, 5, 7, 9 (population)
- Mean = 5
- Squared deviations sum to 32
- σ² = 32 ÷ 8 = 4, σ = 2
Questions people ask
Why divide by n − 1?
A sample's own mean sits closer to its values than the true population mean does, so dividing by n underestimates the spread. n − 1 corrects that.
Is variance ever negative?
No. It's a sum of squares, so it's zero or positive.