It was almost always the case in my childhood that the kids lashing out had bigger problems to deal with at home (parents splitting, drinking or beatings). That was in a mid-lower class mixed town in the 80s-90s elementary school.

We still had a few upper-middle class bullies in there, but they got straightened out when caught, at least until highschool football made it acceptable again and shit got worse for some again. It was also a much bigger highschool.

My wife was in a less diverse school system, more wealthy, and had a much more pleasant experience. Still had to deal with mean girl psychological bullying though in HS.