PALLAS / CALCULATOR
Standard Deviation Calculator
Calculate mean, variance and standard deviation from up to 100,000 values. Choose population or sample semantics explicitly.
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INPUT
Enter values
Method & formula
The engine uses a numerically stable one-pass Welford update for mean and squared deviations. Population variance divides by n; sample variance divides by n - 1.
- Population variance = Σ(x - μ)² / n
- Sample variance = Σ(x - x̄)² / (n - 1)
- Standard deviation = √variance
Example
For 2, 4, 4, 4, 5, 5, 7, 9 as a population, the mean is 5 and the standard deviation is 2.
Sources & standards
FAQ
When should I use sample mode?
Use sample mode when the entered observations are a sample used to estimate the spread of a larger population.
Why does sample mode need at least two values?
Its denominator is n - 1, so one observation does not define a sample variance.