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> Finally, 50% of any group are below average

Not necessarily, but 50% are below the median.

> Not necessarily, but 50% are below the median.

Not necessarily. The numbers could all be the same.

The median is an average.

A lot of people interpret average as meaning "mean". Really average is a stupid ambiguous word that should never be used. Be clear: say mean or median, but never average.

>Finally, 50% of any group are below average.

Yes, language is ambiguous. However, people arguing over the clarity of the above statement is just nerdy pedantry.

I think you meant to say "pedantic nerdery".

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