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Standard Deviation Calculator

Calculate sample and population standard deviation, variance, and coefficient of variation. Standard deviation measures how spread out numbers are from the mean.

Inputs

Sample SD (s, n-1)
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Population SD (ฯƒ, n)
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Sample variance (sยฒ)
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Mean
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Coefficient of variation
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Within 1 SD of mean
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About Standard Deviation Calculator

Sample vs population

When data is a SAMPLE from a larger population, divide by (nโˆ’1) โ€” this corrects bias and gives unbiased estimator. When data IS the entire population, divide by n. Most real-world cases use sample SD.

68-95-99.7 rule

For normally distributed data: ~68% of values lie within 1 SD of the mean, ~95% within 2 SD, ~99.7% within 3 SD. Useful for quick reasoning even when data isnโ€™t strictly normal.

Coefficient of variation

CV = SD รท mean ร— 100%. Unitless โ€” compares spread between datasets with different scales. CV of 10% (tight) vs 50% (highly variable). Useful when SD alone is hard to interpret out of context.