Math

Free Standard Deviation Calculator

Sample and population standard deviation and variance.

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Inputs

Result

Sample standard deviation

1.0954

Population standard deviation1.0000
Sample variance1.2000
Population variance1.0000
Mean4.0000

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Short answer

Sample and population standard deviation and variance.

What is the Standard Deviation Calculator?

Sample and population standard deviation and variance.

How does the Standard Deviation Calculator work?

Enter the inputs above and read the result.

Formula

σ² = Σ(x−μ)² ÷ n; s² = Σ(x−x̄)² ÷ (n−1)

Variables

  • μPopulation mean
  • Sample mean

Explanation

Sample variance divides by n−1 (Bessel's correction) to give an unbiased estimate from a sample.

Examples

Applications

    Advantages

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          Tips

            Related concepts

            The Standard Deviation Calculator sits inside the Math Calculators hub, in the statistics & probability cluster. Describing data and quantifying uncertainty. Understanding the terms below makes the output easier to interpret and easier to compare against neighbouring measures.

            distributiondispersionsignificancesamplepopulationexpected value

            Practical use cases and industry applications

            Understanding Standard Deviation

            Sample and population standard deviation and variance. Within math calculators, standard deviation belongs to the statistics & probability cluster, where it shares terminology and assumptions with closely related tools.

            Learning how standard deviation is calculated

            Sample variance divides by n−1 (Bessel's correction) to give an unbiased estimate from a sample. Working through the variables one at a time — μ, x̄ — makes the result reproducible by hand and easier to sanity-check.

            Using standard deviation to make a decision

            Because outputs depend on the assumptions you enter, run more than one scenario before committing to a figure.

            How standard deviation compares with related measures

            distribution, dispersion, significance, sample all describe adjacent aspects of statistics & probability. Comparing this calculator's output against those measures — using the related tools listed on this page — prevents a single metric from being read in isolation.

            Frequently asked questions

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