Standard Deviation Calculator
Calculate population and sample standard deviation, variance, and mean for any data set. Paste numbers one per line or comma-separated — results and formula shown instantly.
Count
8
Mean
5.0000
σ (population)
2.0000
σ (sample)
2.1381
Variance (pop)
4.0000
Variance (sample)
4.5714
How to use the standard deviation calculator
Paste a list of numbers separated by commas, spaces, or new lines. Both population and sample standard deviation compute live.
Formula & explanation
Variance σ² = Σ(x − μ)² / N (population) or / (N−1) (sample, Bessel's correction). Standard deviation σ = √variance.
Examples
2, 4, 4, 4, 5, 5, 7, 9 → mean 5, σ_pop = 2, σ_sample ≈ 2.138.
Frequently asked questions
- Population vs sample?
- Use sample (N−1) when you have a subset of a larger group; use population (N) when your data is the entire group.
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