Suppose $X = (x_1, ..., x_N)$.
I would like to work with its "population variance" $s^2 = \frac{1}{N}\sum_{i=1}^N{(x_i - \bar{x})^2}$. Writing out this formula inside a longer expression would be distracting.
One way to write it is $s^2 = Var(\{x_i \mid i =1, \dots,N\})$, or even $s^2 = Var(X)$.
Unfortunately these two $Var(\bullet)$ seem to be invalid expressions, since in the first case $\bullet$ is a set rather than a random variable, and in the second case it is a vector.
Is there a way to abbreviate "elementwise vector variance"?
$s^2 = \frac{1}{N}{\lVert X - \bar{X} \rVert}^2$ is somewhat shorter, but it is still quite verbose and it may not be clear that $N$ is the dimension of $X$.