Standard Deviation Calculator
Sample SD, population SD, and variance for any dataset.
Result
Standard deviation (sample)
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Variance
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Mean
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Count
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Sum of squared deviations
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The formula
Sample SD (you have a sample from a larger population):
s = √( Σ(xᵢ − x̄)² / (n − 1) )
Population SD (your data is the entire population):
σ = √( Σ(xᵢ − μ)² / n )
Why "n − 1" for samples
When you use the sample mean instead of the true population mean, you underestimate the squared deviations slightly. Bessel's correction (dividing by n−1) compensates and makes the sample SD an unbiased estimator of the population SD.