σ

Standard Deviation Calculator

How spread out your numbers are around their mean, for a sample or a whole population.

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Result…

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The data is

Sample divides by n − 1; population by n.

 

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How it's calculated

Sample: s = √( Σ(x − x̄)² ÷ (n − 1) )
Population: σ = √( Σ(x − μ)² ÷ n )

The standard deviation is the typical distance of a value from the mean, in the same units as the data. Use "sample" when your numbers are a sample drawn from a bigger group (the usual case); it divides by n − 1 to correct the bias. Use "population" only when you have every member of the group.

Your numbers, step by step

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