Standard deviation s

See also: The basics of probability theory introduction, Variance V

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.

 

Read on: Other moments (measures of shape)

 

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