Why some people have trouble understanding what "on average" means

Some people have made the claim, perhaps even observation, that if you make a statement that says something about the average of a group, and the person you are talking about gives a counter-argument by presenting an exception (as if that exception discredited the claim), then you are dealing with a low-IQ person.

For example, if you say "on average Asian people are shorter than Americans", and the other person objects to it with "but there are very tall Asian people" (or any variant of that), as if that were a counter-argument to the claim, it quite clearly shows that the person doesn't understand what "on average" means.

Such people might even, at some level, know what averaging is, and might even know how to calculate an average (eg. they are able to calculate that the average of 2 and 6 is 4), but somehow their comprehension of what an "average" means or implies does not seem to go beyond the mechanical mathematical calculation (assuming they even understand that part of it).

There's indeed this strange... I suppose instinct among many people that when you say "on average" you are saying "all" and, thus, even one counter-example nullifies the statement. Perhaps when you say "on average" their brains somehow notionally interprets it as something like "the totality of", "the entire group", that the claim encompasses the entire group ie. all the individuals in it.

Or, perhaps, when you say "on average (something)" their brains just skip that "on average" and they just pay attention to the "(something)". Perhaps their brains skip something that they don't fully understand, and thus they interpret the sentence as if it wasn't there. A bit like if you hear a sentence that's complete and coherent but, for some reason, has a word that you didn't quite catch, you usually just interpret what you heard and understood, especially if it makes sense, and you might not stop to wonder what that one unclear word was, and whether it actually completely changes the meaning of the sentence.

This actually happens a lot more often than people realize. When you hear someone speak fast, in real life or for example in a movie, there may be many words that you don't actually fully hear and understand, but which you instinctively deduce from the context. This is so innate and instinctive that we usually don't even pay attention nor notice when it happens (we only notice when we actually don't understand the sentence because of not understanding that one word.)

And yes, this sometimes does mean that you misinterpret what was said. This happens to everybody from time to time. I'm sure that you can recall times when you misinterpreted what someone said, which only became clear later.

However, in the case of not understanding what "on average" means it's usually not a question of not hearing the word correctly. In this case it's about not fully understanding the meaning, and jumping to conclusions.

Curiously, quite often if you then reply that you said "on average, not all", most people will still insist that there's something wrong about what you said even when they kind of understand that "on average" does not mean "all". There's often this strange obsession that even if what you said is correct, it's still wrong.