Standard deviation measures the amount of variation or dispersion in a dataset. A low standard deviation means data points cluster close to the mean; a high standard deviation means they are spread out over a wider range.
σ = √[Σ(xi − μ)² / N] [Population]
s = √[Σ(xi − x̄)² / (n−1)] [Sample]
σ = population std dev, s = sample std dev, xi = each data point, μ (or x̄) = mean of the data, N = population size, n = sample size. Use n−1 (Bessel's correction) for samples to avoid underestimating variability.
Example 1: Dataset: 4, 7, 13, 2, 1 (treat as a sample)
Result: Sample standard deviation s = 4.83
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