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Calculate sample standard deviation, population standard deviation, variance, mean, and sum of squares for any list of numbers.
Accepts comma, space, or newline-separated integers, decimals, and negative values.
| # | Value (x) | Deviation (x − μ) | Squared (x − μ)² |
|---|---|---|---|
| 1 | 2 | -3 | 9 |
| 2 | 4 | -1 | 1 |
| 3 | 4 | -1 | 1 |
| 4 | 4 | -1 | 1 |
| 5 | 5 | 0 | 0 |
| 6 | 5 | 0 | 0 |
| 7 | 7 | 2 | 4 |
| 8 | 9 | 4 | 16 |
| Total | Σx = 40 | Σ(x − μ) = 0 | SS = 32 |
Standard deviation and variance statement report.
Standard Deviation & Variance Calculator. Calculate sample and population standard deviation, variance, mean, and sum of squares for statistical datasets. ZechKit provides this tool completely free and online, optimized for instant, accurate computations directly inside your web browser.
A Standard Deviation Calculator measures statistical dispersion—how widely individual data points spread out around their central arithmetic mean.
Formulas: Population Standard Deviation (σ) = √[Σ(xi − μ)² / N]. Sample Standard Deviation (s) = √[Σ(xi − x̄)² / (n − 1)], where (n − 1) represents Bessel's correction to eliminate sample bias.
Variance: Variance is the squared standard deviation (σ² or s²), representing the average of the squared differences from the mean.
The Empirical Rule (68-95-99.7): In a normal bell-curve distribution, roughly 68% of data falls within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.
