Let $X$ and $Y$ be two i.i.d. random variables. I am interested in the quantity $$m(X):=\mathbb{E}[X|X>Y] - \mathbb{E}[X|X < Y].$$ It is not hard to see that $m(X) \geq 0$ and that $m(X) = 0$ if and only if $X$ is a constant, almost surely.
So, one may think about $m(X)$ as measuring the dispersion of $X$ in a sense.
My question is there a relation between $m(X)$ to other known measures of dispersion such as variance of mean absolute deviation?