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Certified calculator · Version 1

Variance Calculator

Measure dataset dispersion with an explicit population or sample denominator and inspect the corresponding mean and standard deviation.

Variance1.1875
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

Variance is the sum of squared deviations from the mean divided by N for a population or n−1 for a sample.

Formula

σ²=Σ(x−μ)²/N or s²=Σ(x−x̄)²/(n−1)

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 variance requires at least two observations.
  • Population and sample calculations are explicitly distinguished.

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

Why does sample variance use n−1?

The calculator applies the conventional Bessel-corrected sample variance formula when sample mode is selected.

Is standard deviation also available?

Yes. It is the square root of the calculated variance.

Related calculators

Standard Deviation CalculatorCalculate population or sample standard deviation and variance.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.