TimelyScholarFree Tools › Variance & Standard Deviation Calculator
Paste a list of numbers to get the sample and population standard deviation and variance, the mean, standard error and coefficient of variation, with the step-by-step working.
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| Sample standard deviation (s) | 2.1731Divides by n − 1; use for a sample |
|---|---|
| Sample variance (s²) | 4.7222 |
| Population standard deviation (σ) | 2.0616Divides by n; use when you have the whole population |
| Population variance (σ²) | 4.2500 |
| Mean | 14.5000n = 10 |
| Standard error of the mean | 0.6872s / √n |
| Coefficient of variation | 14.99% |
| Sum of squared deviations | 42.5000 |
| Median, minimum, maximum | 14.500, 11.000, 18.000Range = 7.000 |
| x | x − mean | (x − mean)² |
|---|---|---|
| 12 | -2.5000 | 6.2500 |
| 15 | 0.5000 | 0.2500 |
| 11 | -3.5000 | 12.2500 |
| 18 | 3.5000 | 12.2500 |
| 14 | -0.5000 | 0.2500 |
| 16 | 1.5000 | 2.2500 |
| 13 | -1.5000 | 2.2500 |
| 17 | 2.5000 | 6.2500 |
| 15 | 0.5000 | 0.2500 |
| 14 | -0.5000 | 0.2500 |
| Mean 14.5000 | Σ = 42.5000 |
s² = 42.5000 / (10 − 1) = 4.7222; s = √4.7222 = 2.1731
Separated by commas, spaces or new lines.
Sample (n − 1) for a sample; population (n) for a whole population.
The standard deviation measures how spread out values are around the mean; the variance is its square.
When your data are a sample used to estimate a wider population, divide the sum of squared deviations by n − 1 (the sample SD). Divide by n only when you have measured the whole population.
Almost always the sample standard deviation (n − 1), because study participants are a sample of a wider population.