Variance Calculator
Calculate sample and population variance from a list of numbers, with the mean, sum of squared deviations and both standard deviations shown alongside.
Sample variance
31.8095
from 7 values
Sample variance (s²)31.8095
Population variance (σ²)27.2653
Sample SD (s)5.64
Population SD (σ)5.2216
Mean19.8571
Count7
Sum139
Sum of squared deviations190.8571
Variance is in squared units. Take its square root for a figure in the original units.
About the Variance Calculator
Variance measures how far a set of numbers spreads out from its mean, in squared units. Paste or type your numbers separated by commas or spaces; the sample figure is shown first, since that is the one you want unless your numbers are the entire population.
Formula
Population: σ² = Σ(x − μ)² / N. Sample: s² = Σ(x − x̄)² / (N − 1). Subtract the mean from each value, square the differences, add them up, then divide. The sample version divides by N − 1 rather than N, which corrects a bias that would otherwise make the spread look smaller than it is.
Frequently Asked Questions
Standard deviation is the square root of the variance. Variance is in squared units, so a spread of heights in centimetres gives a variance in square centimetres, which is hard to picture. Taking the root returns it to centimetres.
Use the population formula only when your numbers are the whole group you care about, such as every employee in a company. If they are a sample drawn from something larger, which is the usual case, use the sample formula that divides by N − 1.
A sample's own mean sits closer to its data than the true population mean does, so the squared deviations come out slightly too small. Dividing by N − 1 instead of N compensates. This is known as Bessel's correction.
No. Every term in the sum is a squared number, so the total can never fall below zero. A variance of exactly zero means every value in the set is identical.
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