However, there’s a third way to think about the first moment, and it’s the one that I think is most useful for understanding moments generally: the first moment tells us how far away from the origin the center of mass is. I like this interpretation because it is analogous to a moment arm in mechanics, which is the length of an arm between an axis... See more

moments are important theoretically because they provide an alternative way to fully and uniquely specify a probability distribution, a fact that is intuitive if you understand how moment’s quantify a distribution’s location, spread, and shape