# Variance V

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.