Standard Deviation Calculator

Paste your numbers (separated by commas, spaces or new lines) and choose sample or population.

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What standard deviation tells you

Standard deviation measures how spread out numbers are around their average (mean). A small value means the numbers are close together. A large value means they are spread out. Two classes can both average 70 marks, but one with a standard deviation of 5 is much more consistent than one with 20.

Sample or population?

Population (σ): you have every value, for example the marks of all 40 students in a class. Divide by n.
Sample (s): your numbers are a sample from a bigger group, for example 200 survey answers out of a whole city. Divide by n − 1 (Bessel's correction), which gives a slightly larger, fairer estimate.

The formula

s = √( Σ(x − x̄)² ÷ (n − 1) ). Variance is the same without the square root. The calculator also shows the standard error of the mean (s ÷ √n), used for confidence intervals. In Excel, STDEV.S is the sample version and STDEV.P the population version.

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How it works

Enter — type or paste your values or text.
Get the result — it is worked out in your browser.
Adjust — change the inputs to compare, or copy the result.

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