Variance V

See also: Standard deviation, Probability parameters introduction

The variance is a measure of how much the probability distribution is spread from the mean:

            

where  denotes the expected value (mean) of whatever is in the brackets, so:

            

The variance sums up the squared distance from the mean of all possible values of x, weighted by the probability of x occurring. The variance is known as the second moment about the mean. It has units that are the square of the units of x. So, if x is cows in a random field, V has units of cows2. This limits the intuitive value of the variance.

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:  Standard deviation

 

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