Standard Deviation Calculator
Population/sample standard deviation, variance and mean of a list.
How it works
Population σ = √(Σ(x−μ)² ÷ N); Sample s = √(Σ(x−x̄)² ÷ (n−1))
Standard deviation measures spread. Use σ when the data is the whole population, or s (divide by n−1) for a sample.
FAQ
σ or s — which to use?
Use population σ when the data is the entire set; use sample s for a subset. They converge for large samples.
Worked example
Data 2, 4, 4, 4, 5, 5, 7, 9: mean = 5.
Sum of squared deviations = 9+1+1+1+0+0+4+16 = 32.
Sample SD (denominator n−1 = 7): √(32/7) ≈ 2.14; population SD (denominator n = 8): √(32/8) = 2.00.
Notes and limitations
Use n−1 (Bessel’s correction) when estimating a population from a sample, and n when you have the entire population. Two datasets can share a mean but differ sharply in spread, so report the mean together with a measure of dispersion.