- [[statistical moments]] # Idea The standard deviation is a standardized measure of the amount of dispersion or variance in a variable. It is related to the second [[statistical moments|central moment]]. ## Population standard deviation $ \sigma=\sqrt{\frac{\sum\left(x_{i}-\mu\right)^{2}}{N}} $ - $x_i$: data point $i$ - $\mu$: $\bar{x}$, or mean of all $x_i$ - $N$: total number of observations ## Sample standard deviation $ s=\sqrt{\frac{\sum\left(x_{i}-\mu\right)^{2}}{n-1}} $ ## Root mean square Physical scientists often use the term **root-mean-square (RMS)** as a synonym for standard deviation when they refer to the square root of the mean squared deviation of a quantity from a given baseline. # References - [Standard Deviation -- from Wolfram MathWorld](https://mathworld.wolfram.com/StandardDeviation.html)