A: This is perhaps one of the most-oft cited rebukes of racialism.  And because even otherwise intelligent people use it, it is important to know why this statement does not say what most think it does.

      For one, comparing variation "within" and variation "between" is comparing apples and oranges.  What one is comparing in this instance is the ranges of variation with means of variation.  

      Let's use race and IQ for illustrative purposes.  Let's set the average range of IQ scores as being between 40 and 190.  That's a variation of 150 points in both black and white scores.  Undoubtedly the range is bigger but this will serve our purposes.  The average white IQ is 100 and the average black IQ is 85, a difference of 15.

      So filling in the blanks, there is more variation within racial groups (150 points) than between them (15 points), ergo race is a meaningless construct...right?

     Wrong.  The fact of the matter is that IQ scores are not equally distributed along the range but are clustered around the mean in a bell curve shape.  So what we find is that ...  

So

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