Standard Deviation Calculator
Calculate sample and population standard deviations with an itemized deviation table.
Sample Std Dev (\(s\))
5.2372
Variance (\(s^2\)): 27.4286
Population Std Dev (\(\sigma\))
4.8990
Variance (\(\sigma^2\)): 24.0000
Step-by-Step Deviation Table
| i | Value (\(x_i\)) | Deviation (\(x_i - \bar{x}\)) | Squared Deviation (\((x_i - \bar{x})^2\)) |
|---|
Standard Deviation Formulas & How to Calculate
View All Math Formulas Handbook →Sample Standard Deviation ($s$)
Unbiased estimate with $n - 1$ degrees of freedom:
$$ s = \sqrt{\frac{1}{n - 1} \sum_{i=1}^{n} (x_i - \bar{x})^2} $$
How to calculate:
$$ s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1}, \quad s = \sqrt{s^2} $$
Population Standard Deviation ($\sigma$)
Used when evaluating the full population $N$:
$$ \sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2} $$
How to calculate:
$$ \sigma^2 = \frac{\sum (x_i - \mu)^2}{N}, \quad \sigma = \sqrt{\sigma^2} $$