This possibly should be posted as comment on answer here, but I do not have enough reputation points: Difference between Variance and 2nd moment. The formula for calculating variance goes as follows:
$$ \operatorname{Var} (X) = {\Bbb E} \left( X^2 \right) - \left( {\Bbb E} (X) \right)^2 $$
I have seen (and done) algebraic development of that formula, but that is just a bunch of symbols with that formula falling out on the right side after the last equal sign. My question is about the intuition behind that (the "3blue1brown-kind-of-explanation" of it)?
I have also done a lot of googling, but the only thing going remotely towards the answer is this video. But it is again just a lot of symbols and no intuition. However, understanding the formulas there may lead towards the answer?
