Tiers of Ability, Part 1

     Bruce Charlton made an astute observation in a comment on this post:

        "mathematical and musical abilities seem more varied than anything else I know of.

(And I think there is a surprising positive between music composition and maths.)

Most people are pretty close to zero! - and then the people who are good are So much better - and then there are some who are So much better than the people who are good...

But the distribution doesn't seem anything like a bell curve - more like something very positively skewed.


The famous Bell Curve
A negatively and positively skewed distribution
    The Bell Curve is symmetric.  Whatever population we are examining, if a trait is distributed normally within the population, then there will be as many members of the population who have the trait a given distance above the average as there are who have the trait a given distance below average.  However, with positively and negatively skewed distributions, more members of the population are either above the mean or below the mean respectively.  
    So, Bruce Charlton makes the point that because the range of mathematical and musical ability is so large most people are at the low end of the spectrum with a very small number of people at the high end.  But not only that, there are large gaps between each of the levels, so the best way we can conceptualize this is by tiers of ability. 

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