An example of over-generalization would be, "Farmers I've met have been pretty slow to pick up on new ideas." Of course, for this to be over-generalization a necessary criteria would be that the speaker had only met a few farmers. How many would depend on the level of the generalization. In this example a large sample would be necessary.

Example where the speaker used over-generalization

I'll tell you something, they are all like that, they are only interested in one thing and that is themselves, kids now-a-days are just plain selfish. If we let one, even one, of them get started doing something they shouldn't then we'll be in trouble and you'll be able to see the handwriting on the wall, the gangs will be in here and it'll be all over.