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

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