Statistics lab
Compute population or sample standard deviation, view summed steps, and review formulas, margin-of-error tables, and frequency summaries, mirroring calculator.net’s descriptive layout.
Standard deviation, typically denoted by σ, is a measure of variation or dispersion (refers to a spread of data). A low value indicates that data points tend to be close to the mean of a set, while a high value indicates the data are spread out over a wider range. This calculator supports both population and sample standard deviation and displays the variance and mean alongside the final result.
For an entire population, use the formula σ = √( Σ (xᵢ − μ)² / N ), where μ is the mean and N is the number of values. Example: values (1, 3, 4, 6, 9) → μ = 4.6 → σ ≈ 2.87.
When a population cannot be fully measured, use s = √( Σ (xᵢ − x̄)² / (n − 1) ). The (n − 1) term is Bessel’s correction, making the sample estimate unbiased. Example: values (2, 4, 4, 4, 5, 5, 7, 9) → mean 5 → s ≈ 2.
Standard deviation gauges variation from the mean. Engineers monitor manufacturing processes, scientists quantify measurement uncertainty, and finance teams assess volatility. Knowing how spread out data are helps determine whether results meet expectations or warrant further investigation.