Variance Calculator

Enter numeric data to calculate population variance, sample variance, and the sample mean using unbiased formulas.

Data values (separate with spaces or commas)

Count

Mean

21.0000

Population variance

36.0000

Sample variance

42.0000

Interpretation

Population variance: Use when you analyze an entire population. Denominator n keeps every observation weighted equally.

Sample variance: Use when your data is a sample from a broader population. Bessel's correction (n − 1) removes bias.

Enter the dataset using spaces or commas to separate numbers.
Review the computed mean, population variance, and sample variance.
Use sample variance for inferential statistics and population variance when you have complete data.
Take the square root of variance to obtain standard deviation if needed.

Mean μ = Σx / n

Population variance σ² = Σ(x − μ)² / n

Sample variance s² = Σ(x − μ)² / (n − 1)

Standard deviation = √(variance)

Sample variance uses n − 1 (Bessel's correction) to provide an unbiased estimator of population variance when working with samples.

Sample variance adjusts for missing population data, making it unbiased when estimating population variance.

No. Variance sums squared deviations, so it is always zero or positive.

Variance is defined for any numeric distribution, though some inference procedures assume approximate normality.

Standard deviation is the square root of variance, bringing dispersion back to the original units of measurement.