Variance Calculator

Calculate population and sample variance for a data set.

What the Variance Calculator does

Variance measures how far values sit from the mean, averaged over squared distances. Squaring stops positive and negative deviations from cancelling, but it also means variance is expressed in squared units — which is why the standard deviation is usually quoted instead.

Formula

  • Population: σ² = Σ(x − μ)² ÷ n
  • Sample: s² = Σ(x − x̄)² ÷ (n − 1)

Inputs explained

InputUnitRequiredNotes
NumberstextYesSeparate values with commas, spaces or new lines.
Data set typeone of 2 optionsYes

How to use it

  1. Choose Data set type.
  2. Enter Numbers.
  3. Select Calculate.

Worked example

Sample measurements of 4, 8, 6, 5 and 3.

Numbers
4, 8, 6, 5, 3
Type
Sample

Mean 5.2, squared deviations sum to 14.8, so s² = 14.8 ÷ 4 = 3.7.

Frequently asked questions

Why divide by n − 1 for a sample?

Because the sample mean sits closer to your data than the true population mean does, which understates spread. Dividing by n − 1 — Bessel's correction — removes that bias.

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