Imagine I want to statistically characterise a set of converging points and still get an idea of the converging properties or shape of such set, for example
The values of the mean or variance of the $y$ coordinates don't really tell me anything specific about the converging shape of such set and I wouldn't be able to, just by looking at such values, distinguish the previous set from something like
I could, however, artificially build something depending on the $x$ coordinates (the variance, for example). Naturally, in the first set, for points where $x>L$, we expect the variance of the $y$ coordinates to decrease as $L$ increases, but this seems too much, so I was wondering if there is a neater way of statistically characterising such sets and being able to distinguish both previous sets. Any ideas?