Jim Henderson wrote:
> On Wed, 21 Jul 2010 13:58:06 -0400, Warp wrote:
> 
> 
>>   If the curve of people's intelligence is not linear, it can mean that
>> the majority of people are actually below average than above it (or the
>> other way around, of course, depending on the sign of the derivative of
>> the curve).
> 
> For a large statistical sample, IIRC, it's basically a bell curve.

It depends on what it's a statistical sample of.  It only comes out a 
bell curve under certain assumptions about how what you're sampling 
behaves, and these will not hold in many circumstances.

That said, I think IQ tests do tend to come out more or less a symmetric 
distribution (and close to a bell curve) so pretty close to half of the 
population will indeed be below average, so the theoretical point Warp's 
making doesn't really apply in this case.

> 
>>   As a simple example, if we have 4 people with IQs 90, 90, 90 and 130,
>> the average will be 100, but the majority of these people is below
>> average. In other words, three quarters of the people are "stupid" and
>> one quarter is "smart".
> 
> Except that when measuring "average" intelligence, your sample size is a 
> population, not a small discrete number.
> 

It turns out that Warp's overall point is correct in this case, and you 
can also generate examples for continuous probability distributions. 
This occurs in cases where the distribution is asymmetric (see 
http://en.wikipedia.org/wiki/Skewness).  I'm not sure what he meant by 
"the sign of the derivative", but maybe this was what he was thinking about.

I don't totally see how it applies to the conversation since "stupid" 
and "smart" in this context haven't been given rigorous definitions, but 
if you are to define them by which side of the IQ median you lie on, 
then he would be correct if the IQ distribution were asymmetric (which 
it mostly doesn't seem to be).

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