Variance Calculator
Calculate population and sample variance of a data set, with mean and squared deviations.
Enter your data set. Invalid values will be ignored.
Variance
Mean (x̄)
Count (n)
Sum of Squared Deviations (SS)
Standard Deviation
Formula Used
What Variance Measures
Variance measures how far a set of numbers is spread out from their average value. It is the average of the squared differences from the mean. A small variance indicates that the data points tend to be close to the mean, while a large variance indicates the data is spread out over a wider range of values.
Population vs Sample Variance
Population variance (σ²) divides the sum of squared deviations by n and is used when your data includes every member of the group you care about. Sample variance (s²) divides by n − 1 and is used when your data is only a sample drawn from a larger population.
- Population: σ² = Σ(xᵢ − x̄)² / n
- Sample: s² = Σ(xᵢ − x̄)² / (n − 1)
Bessel's Correction (n − 1)
When estimating the variance of a population from a sample, dividing by n tends to underestimate the true variance. Dividing by n − 1 instead, known as Bessel's correction, produces an unbiased estimator. This is why the sample variance requires at least two values, and the standard deviation is simply the square root of the variance.