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Bugmaster comments on Undiscriminating Skepticism - Less Wrong
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I think this is, in fact, a common statistical fallacy: using the mean instead of the median to represent "average".
Median is often better, but not always - it depends on the purpose you wish to put the data to. With anything less than the full distribution, you'll be able to hit some cases in which it can mislead you.
Edited to add:
Specifically - if you are interested in totals, mean is usually a more useful "average". Multiplying the total number of water balloons by the average amount of water in a balloon gives you a much better estimate (exact, in theory) with mean than with median. If you are interested in individuals, median is usually better; if I am asking if the next water balloon will have more than X amount of water, median is a much more informative number. Neither is going to well represent a multimodal distribution, which we might expect to be dealing with in the great*-grandparent's case anyway if the hypothesis of a strong genetic component to variation in intelligence does in fact hold.
Good point. You should select a metric that would be most useful in any given situation, be it the mean, the median, or anything else.
Ah; so I'm misunderstanding what brazil84 means by average?
No, I think his example of 5 ethnic groups is flawed, because he's using the wrong metric to calculate the average. If he was using the median instead of the mean -- which is the right thing to do in this case -- he'd obtain the result that "most blacks have average intelligence", and his conclusion would no longer follow.
(Edited: typo)
The 5 ethnic groups was mine originally.
But then I have to consider the scenario where the median gives the result of below averge intelligence - will take me slightly longer to puzzle out in my head.