Variance

The variance measures how much spread out the mean of a distribution is. It computes that by measuring the expected value of difference between the mean and the actual value of the random variable, squared.

The square is useful to get always a positive number.

$$\text{Var}(X)=\mathbb{E}[(X-\mu {)}^2]$$

If we take the square root of this value, we obtain the Standard Deviation, which is another way of measuring the spread of the distribution.

Note

If two variables $X$ and $Y$ are independent, then:

$$\text{Var}(X+Y)=\text{Var}(X)+\text{Var}(Y)$$

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statistics