What is Sigma over x?

Question

What does $\sum_xx$ mean?

I'm used to $\sum_{i=1}^{n}$, but what's the above?

Update: I find in our statistics book these notations:

$$\sum_{x}|x-\tilde{a}|f(x)$$

Answer 1

The summation notation varies a lot but from what I can tell, the one you're showing us is simply a contraction, mainly: $$\sum_x x = \sum_{x=0}^{\infty}x$$ that has meaning if $x\in\mathbb{N}$. But if $x$ is in some sort of set, like $x\in X$ surely the notation is used as a contraction for $$\sum_{x\in X}x = \sum_x x$$ like, for example, if $X = \left\{10,22,35,55.5,\pi\right\}$ the sum should be $$\sum_x x = 10+22+35+55.5+\pi$$ so the sum on all the possible value that $x$ can have

Edit

By telling us where you found that notation is clear that yes we are summing over a set of possible value for $x$. I'm not a statistician but from what I recall $$Var[x] = \sum_x (x-\bar{x})^2f(x)$$ so you have a certain set of measurement, for example, and this measurement follows a certain PDF $f(x)$. To calculate the variance you sum over all the measured value of $x$ in your statistical set according to that formula