Calculate sample and population standard deviation, variance, mean, and sum of squares.
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σ = √[Σ(x - μ)² / N] (Population) | s = √[Σ(x - x̄)² / (n - 1)] (Sample)
Values: 10, 12, 23, 23, 16, 23, 21, 16 (Sample mode).
Sample Std Dev (s): 5.237 | Variance: 27.429 | Mean: 18.00.
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Open calculatorUse population standard deviation (σ) when your dataset contains every single member of the entire group. Use sample standard deviation (s) when your data represents a random sample taken from a larger group (Bessel's correction n-1).
It quantifies the amount of dispersion or variation in a dataset. A low standard deviation indicates values cluster close to the mean, while a high standard deviation indicates spread over a wider range.
Standard deviation is the benchmark metric for risk analysis in finance (volatility), experimental error in physical sciences, and quality assurance in manufacturing (Six Sigma).