Standard Deviation Calculator
Calculate standard deviation, variance, and mean from a set of numbers.
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Standard Deviation
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Mean
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Variance
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Sample Std Dev
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What Is Standard Deviation?
Standard deviation measures the amount of variation or spread in a set of values. A low SD means values are close to the mean; high SD means they're spread out.
Formula
σ = √(Σ(xᵢ − μ)² / N) for population, s = √(Σ(xᵢ − x̄)² / (n−1)) for sampleExample
For values {10, 12, 23, 23, 16, 23, 21, 16}: Mean = 18, SD = 4.898.
Frequently Asked Questions
Population vs sample standard deviation?
Use population (÷N) when you have all data points. Use sample (÷(n−1)) for a subset of a larger population.
What does standard deviation tell me?
About 68% of data falls within 1 SD of the mean, 95% within 2 SDs, and 99.7% within 3 SDs (for normal distributions).