As I understand it, variance of a random variable is defined as follows: \begin{equation} \text{Var}(X) = \text{E}[(X-\mu)^2] \end{equation} $X-\mu$ is obviously the difference between the value of the random variable and the expected value of the random variable.
Why don't we define variance as \begin{equation} \text{Var}(X) = \text{E}[X-\mu] \end{equation}
To me, this would make more sense because it would express the difference between the expected value and the value it takes...which to me sounds like variation.
Why do we use the $(X-\mu)^2$ instead?
