Standard Deviation Calculator
Calculate standard deviation and variance for any dataset
About Standard Deviation
What is Standard Deviation?
Standard deviation measures how spread out numbers are from the mean. A low standard deviation indicates values are close to the mean, while a high standard deviation indicates values are spread out.
Formulas:
Population Standard Deviation:
σ = √[Σ(xᵢ - μ)² / N]Sample Standard Deviation:
s = √[Σ(xᵢ - x̄)² / (n - 1)]Sample vs Population
- Population: Use when you have data for the entire population
- Sample: Use when you have a subset and want to estimate population parameters
- Sample standard deviation uses (n-1) to provide an unbiased estimate (Bessel's correction)
Empirical Rule (68-95-99.7)
For normally distributed data:
- 68% falls within ±1 standard deviation
- 95% falls within ±2 standard deviations
- 99.7% falls within ±3 standard deviations
About This Calculator
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