Statistics

Confusing Standard Deviation and Variance

Students report the variance as the standard deviation, or they forget to take the square root.

Quick check

Why students make it

Both measures describe spread, so they can feel like two names for the same idea. The squared deviations in the variance formula also make students lose track of the units.

The rule done right

Variance is the average squared distance from the mean, so its units are squared. Standard deviation is the square root of variance, so sigma = sqrt{sigma^2} for a population and s = sqrt{s^2} for a sample.

Related resources

standard-deviationvariancespread