Standard Deviation Calculator

What standard deviation measures

Standard deviation tells you how spread out values are around their mean. To calculate it: find the mean, subtract the mean from each value, square those differences, average them, and take the square root. For a population you divide by N; for a sample drawn from a larger group you divide by n − 1 (Bessel's correction), which slightly increases the result to correct for sampling bias.

A small standard deviation means values cluster tightly around the mean; a large one means they are widely scattered.

Worked example

For the values 4, 8, 6, 5 and 7, the mean is 6. The deviations are −2, 2, 0, −1 and 1, whose squares add to 10. Population variance is 10 ÷ 5 = 2, so σ = 1.414. Sample variance is 10 ÷ 4 = 2.5, so s = 1.581.

Interpreting the result

For roughly bell-shaped data, about 68 percent of values fall within one standard deviation of the mean and about 95 percent within two. Standard deviation is sensitive to outliers, so a single extreme value can inflate it; check your data for errors before relying on the figure.