/sci/ - Science & Math

Why is statistics so convoluted and unaesthetic?
Even some of the most basic statistical principles are built up on mountains of elaborate and obscure derivations that almost nobody using them today has any understanding of.

This question sounds retarded but I actualy don't understand it. I've never taken a rigourous probabilty course but I'm well established in other fields of maths.But, why is the pic related function "normal"?

I mean I understand the "shape" as to why use an e^-(x^2) function to get a sort of bell curve. But how do you derive the pi factors and where to place variance and the mean? I mean why is there 1/sqrt(2pi) in there?

You could also formulate it as why does it have to have does parametres of probability (around 30% between the first standard deviation and so on). What of all that makes it standar and "organic" in the sense that it fits many data models?