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Standard Deviation Calculator
Compute the mean, variance, and both population and sample standard deviations from a list of numeric values.
How the Standard Deviation Calculator Works
This calculator computes the mean, variance, population standard deviation, and sample standard deviation for a set of numbers. Standard deviation measures how spread out the values in a dataset are relative to their average.
Formula Used
Population SD (σ) = √[Σ(x − μ)² ÷ N]
Sample SD (s) = √[Σ(x − x̄)² ÷ (n − 1)]
- x
- — each individual value in the dataset
- μ / x̄
- — the arithmetic mean (average) of the values
- N / n
- — the total number of values in the dataset (N for population, n for sample)
Example Calculation
For a dataset [10, 12, 23, 23, 16, 23, 21, 16] (mean = 18): Variance = 24. Population Standard Deviation = √24 = 4.8990. Sample Standard Deviation (dividing by n-1 = 7) = 5.2372.