Standard Deviation Calculator
Calculate population and sample standard deviation. Enter your data set for instant results with mean and variance.
Std Deviation
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Variance
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Mean
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Standard Deviation Formulas
Population Standard Deviation (σ)
σ = √( Σ(xᵢ − μ)² / N )
Sample Standard Deviation (s)
s = √( Σ(xᵢ − x̄)² / (n−1) )
Data: 2, 4, 4, 4, 5, 5, 7, 9 (n=8, mean=5)
Population σ = 2
Population σ = 2
Population vs Sample
Use population when you have data for the entire group. Use sample when your data is a subset (the denominator changes to n−1, known as Bessel's correction).
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Last updated: 2026-08-08