How does the Standard Deviation work?

Find the mean x̄ Then: Subtract the mean from each value and square the result: (xᵢ − x̄)² Then: Average the squared differences (÷n for population, ÷(n−1) for sample) Then: Take the square root.

Can you give an example of how to use the Standard Deviation?

Example: Input 2, 4, 4, 4, 5, 5, 7, 9 gives a result of σ = 2.0, mean = 5 (Population std dev).

Is the Standard Deviation free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Standard Deviation?

Our Standard Deviation uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Standard Deviation

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Standard deviation measures how spread out the values in a dataset are from the mean. A low standard deviation means values cluster tightly; a high one means they are spread out. It is the square root of variance.

Range	Contains ~% of data
Mean ± 1σ	68.27%
Mean ± 2σ	95.45%
Mean ± 3σ	99.73%

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Did You Know?

Six Sigma is a quality standard meaning 99.99966% of products are defect-free — only 3.4 defects per million opportunities. It gets its name from 6 standard deviations from the mean.

References

›Standard deviation — Wikipedia
›Standard deviation — Khan Academy

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Standard Deviation Explained: Formula, Examples & When to Use It

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Statistics for Beginners: Mean, SD, Hypothesis Tests, and More

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Normal Distribution (Bell Curve)

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