Standard Deviation Calculator

Sample and population standard deviation, variance and summary statistics for your data.

Choose sample when your data is a subset of a larger group.

Enter your details and press Calculate to see results.

Formula

σ² = Σ(x − x̄)² / n (population) · s² = Σ(x − x̄)² / (n − 1) (sample)

Example

For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the population standard deviation is exactly 2.

What standard deviation tells you

Standard deviation summarizes how spread out values are around the mean. Small σ means values cluster tightly; large σ means they scatter widely. For roughly normal data, about 68% of values fall within one standard deviation of the mean.

Sample vs population

When your data is a sample used to estimate a bigger population, dividing by n−1 (Bessel's correction) gives an unbiased variance estimate. Use the population form only when you truly have every member of the group.

Frequently asked questions

What does a standard deviation of zero mean?

Every value in the data set is identical.

Can standard deviation be negative?

Never. Squared deviations are non-negative, so their square root cannot be either.

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