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To be pedantic, most people usually mean "median" (or a robust estimation of the mean without considering outliers) by average, and in samples from a continuous distribution it is necessarily true that ~50% are above/below the median.

You are not being "pedantic". You are being wrong.

There's no reason to assume that commonly mean means median or that there are enough properties to make them equal.

Besides a claim about "most people" without some solid data is poor support for anything.

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