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Standard Deviation Calculator

Compute mean, variance, and standard deviation from a comma-separated list with sample (n−1) or population (n) mode.

Clear formulas
Educational steps
Detail breakdown

Spread calculator with explicit sample vs population denominators.

Limitation: Educational statistics.

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How to Use the Standard Deviation Calculator

Spread calculator with explicit sample vs population denominators.

1

Open the Std Dev calculator and read field labels.

Match the mode

Educational statistics.

What It Calculates

Spread calculator with explicit sample vs population denominators.

Worked Examples

Sample SD classic set

Inputs

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

Result

s ≈ 2

Textbook sample SD example.

Population same list

Inputs

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

Result

σ ≈ 1.87

Denominator n instead of n−1.

Simple spread

Inputs

numbersText:10, 12, 14
mode:sample

Result

s = 2

Evenly spaced trio.

Check your mode

Educational statistics.

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

s ​=​ √​(​Σ​(​x−x̄​)​²​/​​(​n−1​)​​)​

Scientific Background

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

Sources & review

Standard Deviation 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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