Variance Calculator
Sample and population variance from any list of numbers, with the standard deviations alongside.
The formula
s² = Σ(x - x̄)² / (n - 1)
Subtract the mean from each value, square the differences, add them up, and divide by n - 1 for a sample (or n for a full population). For 4, 8, 6, 5, 3, 7 the mean is 5.5 and the sample variance is 3.5.
Variance vs. standard deviation
Standard deviation is just the square root of variance, and it lives in the same units as the data, which makes it the number people quote. Variance is what the math prefers: variances of independent quantities add, which is why portfolio risk, measurement error budgets and ANOVA all work in variance and convert to standard deviation only at the end.