Variance Calculator

Variance measures how spread out a set of numbers is around its mean, by averaging the squared distance of each value from that mean. Standard deviation, its square root, brings the units back to match the original data — which is why standard deviation is usually the number quoted, with variance as the intermediate step.

Sample vs population variance

Use population variance (divide by n) when the data set is everything you care about — every student in a class, every part in a finished production run. Use sample variance (divide by n − 1) when the data is a subset standing in for a larger population — a survey of 200 customers out of a customer base of 50,000. Dividing by n − 1, known as Bessel's correction, corrects a slight downward bias that comes from estimating the mean from the same data.

Reading the result

A low variance means values cluster tightly around the mean; a high variance means they're spread widely, with the same mean potentially hiding very different underlying data. Two data sets can share an identical average and completely different variances — which is exactly why variance is reported alongside a mean rather than instead of it, in test scores, quality control and financial risk analysis alike.