The Corner

Means and Medians

From a reader (and Poli Sci Prof):

I know you don’t actually care, but you were almost certainly

right the first time.

If half the population has a below-median intelligence (true

by definition);

If intelligence has a lower bound (0 IQ/ brain death/ etc) but

no necessary upper bound, or even just an upper bound that is

further above the median than 0 is below it and that trails

off gradually (i.e. there are geniuses and a few super-geniuses);

and if intelligence has an otherwise roughly-normal

distribution (a bell curve, which is a perfectly ordinary

fact of probability and carries none of the baggage of The

Bell Curve);

In short, if the distribution of intelligence is a

left-censored bell curve (a bell curve truncated at 0 on one

side but exhibiting normal trailing-off properties on the other);

then mean intelligence is higher than median intelligence.

From this it follows that *more* than half the population has

below-average (meaning, as your correspondent insists,

below-mean) intelligence.

Really.

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