What's wrong with stereotypes?

The line between stereotype and cultural averages needs to be better understood by a wide range of people. There's a tendency to call cultural averages stereotyping, which is either failure of the speaker to make clear their parallel understanding of intra-societal variation, or their ignorance thereof, or the ignorance thereof of the receiver.
 
What is cultural averages? We could understand it better if you would provide a definition. By the way I never heard of it...

If half of the Irish is a drunkard and the other half is a teetotaler, than on average, the Irish are average/normal drinkers....
 
You could say "a lot more Canadians per capita play hockey than the Irish", making it a comparison of percentages. As a lot of things, it's relative to some other group. If you say it's uniform, as Tiassa comments above, then it's stereotyping.
 
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