Standard deviation s | Vose Software

# Standard deviation s

The standard deviation is the positive square root of the variance, i.e. s = √V. Thus, if the variance has units of cows2, the standard deviation has units of cows, the same as the variable x. The standard deviation is therefore more popularly used to express a measure of spread.

### Example

The variance V of the Uniform(1,3) distribution is calculated as follows:

from here

and therefore

and the standard deviation s is therefore:

Variance and standard deviation have the following properties, where a is some constant and X, Xi are random variables:

 and
 and
 providing the Xis are uncorrelated.