# Standard Deviation

Written by Jerry Ratzlaff on . Posted in Algebra

Standard deviation, abbreviated as $$sigma$$ (Greek symbol sigma), measures how spread out the data is.

## Standard Deviation formulas

 $$\large{ \sigma = \sqrt{ \frac{ \sum \; \left( X_s \;-\; m \right)^2 }{ n } } }$$ $$\large{ \sigma = \sqrt{ \frac{ 1 }{ n } \; \sum_{s=1}^n \; \left( X_s \;-\; m \right)^2 } }$$

### Where:

$$\large{ \sigma }$$ = standard deviation

$$\large{ \sum \;X_s }$$  (Greek symbol Sigma) = sum of data values  $$\large{ X_1, X_2, X_3, ... }$$

$$\large{ m }$$ = mean value

$$\large{ n }$$ = number of data values