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Variance Calculator

Calculate variance and standard deviation from a numeric list with clear sample vs population choice.

Clear formulas
Educational steps
Detail breakdown

Variance with paired SD output and mean/count details.

Limitation: Educational statistics—not survey weighting or robust estimators.

Jump to calculator · Sources & review

How to Use the Variance Calculator

Variance with paired SD output and mean/count details.

1

Open the Variance calculator and read field labels.

Match the mode

Educational statistics—not survey weighting or robust estimators.

What It Calculates

Variance with paired SD output and mean/count details.

Worked Examples

Sample variance

Inputs

numbersText:2, 4, 4, 4, 5, 5, 7, 9
mode:sample

Result

s² ≈ 4

Square of sample SD.

Population variance

Inputs

numbersText:10, 20, 30
mode:population

Result

σ² ≈ 66.67

Divide by n = 3.

Constant list

Inputs

numbersText:5, 5, 5
mode:population

Result

0

No spread.

Check your mode

Educational statistics—not survey weighting or robust estimators.

Frequently Asked Questions

Yes. Results keep the precision shown on the page unless the engine requires integers.

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Formulas

Standard definitions with assumptions noted below.

Formula

σ² ​=​ Σ​(​x−μ​)​²​/​n

Scientific Background

Standard statistics definitions with assumptions stated on-page. Educational only—not professional certification.

Sources & review

Variance Calculator documents the references behind its formulas and assumptions. Always treat results as educational estimates, not personalized professional advice.

Last reviewed

July 22, 2026

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