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Reminds me a joke by Robert Anton Wilson:

"You know how dumb an average American is. Well, mathematically speaking, half of them are even dumber than that."

Although by "average" you usually refer to the mean, not the median.

In common English, I would say that "average" as used in the quote is understood to be something closer to mode, hence why the joke works, because it trades on the ambiguity of "average" and the difference between mode and mean.

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