You could just make a stereotype, but it would be like making up a new word that only you use. There's nothing official to say what is or isn't an English word, so technically it would be. Just no one would care. In other words, the hippopotamus stereotype analogy just doesn't work.
You're sort of thinking of 'generalisation', not stereotype, anyway.
It was a long-shot hypothetical statement. Admittedly, it was a bit out there since I wanted the most random example I could think of. Though, I wasn't wrong in saying that Hippopotas is a stereotype for hippopotamuses, since -- and I'm still going to stand by this -- a stereotype consists of several things:
(1) a group which recognizes it
(2) an object to stereotype
(3) a standardized image regarding its attributes or image
stereotype n.
1. A conventional, formulaic, and oversimplified conception, opinion, or image.
2. A person who is regarded as embodying or conforming to a set image or type.
By your definition, a stereotype still IS a generalization because it is a "conventional, formulaic, and oversimplified" thing. It takes the attributes of one thing and
generalizes it to other things of the same category. If a group of things follows a "convention" or a "formula," then they are the same, therefore a "generalization." If you "generalize" something, then you "oversimplify" it.
The second definition isn't exactly relephant elephant either, since that's more of a sociological thing where one embodies a stereotype -- it's one of those words which has retrospective definitions grounded in its own definition only. It would have been more apt to say "2. a person or thing embodying a stereotype," but you can't use the same word in its own definition.
generalize v. (object)
1. to infer (a general principle, trend, etc.) from particular facts, statistics, or the like.
2. to infer or form (a general principle, opinion, conclusion, etc.) from only a few facts, examples, or the like.
3. to give a general rather than a specific or special character or form to.
4. to make general; bring into general use or knowledge.
The key definitions are the third and fourth, in which a "general," or nonspecific, all-encompassing, dare-I-say "conventional, formulaic, and oversimplified" quality is given to something. And if you're still worried about the wording of "conventional, formulaic, and oversimplified," well if a group of things is thought to have all the same attributes, is it not "conventional, formulaic, and oversimplified"? There's conformism, so yes it is. It's formulaic in the same reason -- things in the category in which the generalization is displayed are thought to be in the same "formula." That is, their qualities are the same (and I will refrain from repeating this sentence once again to show the similarity between it and stereotype). The oversimplification is simply the idea that there are no unique characteristics to individual bodies within the group, which sounds pretty much like generalization to me.
Furthermore, I
still like Dictionary.com's definition a whole lot more;
stereotype n. Sociology
a simplified and standardized conception or image invested with special meaning and held in common by members of a group:
Because, you're right. A stereotype has no meaning without a group to believe in or enforce it. "Standardized" is just another word for "generalized." They both involve an idea of universality and acceptance within the grander scheme. The only real difference is that "standardized" falls more into the "formulaic" category, whereas "generalized" falls more into "oversimplified." I feel that both fit the "conventional" part spot on, though.