$ \begin{align*} \sigma &= \sqrt{\frac{1}{N}\sum_{i = 1}^{n}(x_i - \mu)^2} \\ s &= \sqrt{\frac{1}{n - 1}\sum_{i = 1}^{n}(x_i - \bar{x})^2} \end{align*} $ The standard deviation of the [[Math/Probability and Statistics/Dataset|dataset]] of a [[Population|population]] is a [[Statistic|statistic]] that measures its [[Math/Probability and Statistics/Distributions/Dispersion|dispersion]], denoted as $\sigma$/$s$, and calculated as the square root of the [[Variance|variance]]. For the case of samples instead of populations, divide by the sample size minus one to demonstrate [[Uncertainty|uncertainty]]. Multiplying a dataset by a constant multiplies the standard deviation by that constant.