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Certified calculator · Version 1

Standard Deviation Calculator

Enter a dataset and explicitly choose population or sample treatment to calculate its mean, variance and standard deviation.

Standard deviation1.08972473589
Mean2.25
Variance1.1875
Standard deviation1.08972473589
Count4
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Result methodology

Deterministic population dispersion using the explicit N denominator.

Solution steps
  1. Mean = 2.25
  2. Population variance = 1.1875
  3. Standard deviation = √variance = 1.0897247358851685

How this calculator works

Population variance divides squared deviations by N. Sample variance uses the Bessel-corrected denominator n−1. Standard deviation is the square root of the selected variance.

Formula

σ=√variance or s=√sample variance

Computes population or sample dispersion explicitly according to the selected denominator.

Worked example

Population 1,2,3 is a verified test case used by the calculation engine.

Assumptions and limitations

  • Dataset values are finite real numbers.
  • Sample mode requires at least two observations.
  • The population/sample selection determines the denominator and is never inferred.

Methodology & sources

This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint.

  • CalcuMint deterministic statistics engine

Frequently asked questions

What is the difference between sample and population mode?

Population variance divides by N; sample variance divides by n−1.

Does the calculator also show variance?

Yes. Variance and the corresponding standard deviation are calculated from the same dataset.

Related calculators

Variance CalculatorCalculate population or sample variance with supporting standard deviation.Mean Median Mode Range CalculatorCalculate mean, median, mode, minimum, maximum and range from a dataset.Z-Score CalculatorStandardize a value using a supplied mean and positive standard deviation.