Free & Instant
Standard Deviation Calculator
Calculate standard deviation and variance for any data set instantly.
Standard Deviation Calculator
Calculate standard deviation instantly.
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Standard Deviation
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Mean
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Variance
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What is Standard Deviation?
Standard deviation measures how spread out numbers are from their average (mean). A low standard deviation means values are clustered close to the mean, while a high standard deviation means they're spread over a wider range.
Standard Deviation Formulas
Population: σ = √[Σ(x − mean)² / N]
Sample: s = √[Σ(x − mean)² / (n − 1)]
Frequently Asked Questions
What's the difference between population and sample standard deviation?
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Population standard deviation is used when your data represents the entire group of interest. Sample standard deviation is used when your data is a subset, and it divides by (n-1) to correct for bias.
What does variance mean?
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Variance is the standard deviation squared — it represents the average of squared differences from the mean, in the same conceptual sense but a different unit scale.
Where is standard deviation used in real life?
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It's widely used in finance (measuring investment volatility), quality control (manufacturing consistency), and research (understanding data variability).