Billie from Ockham wrote:http://i62.tinypic.com/1zb827l.jpg
The point of the above and the correct use of the above is to demonstrate how small (horizontal) differences in the mean can produce large (vertical) differences in the tails.
That's certainly one of the uses.
Pinker elaborates on it in some detail:
Pinker wrote:With some other traits the differences are small on average but can be large at the
extremes [in compared population distributions]. That happens for two reasons. When two bell curves partly overlap, the farther out along the tail you go, the larger the discrepancies between the groups. For example, men on average are taller than women, and the discrepancy is greater for more extreme values. At a height of five foot ten, men outnumber women by a ratio of thirty to one; at a height of six feet, men outnumber women by a ratio of two thousand to one.
Might be interesting to see how those differences in the tails depend on differences in the mean, even for distributions that have the same standard deviations. Which I think Pinker argues is generally not the case for men and women.
Billie from Ockham wrote:That's it. Nothing more. Using it for other purposes is as ignorant as calling inferential statistics "descriptive" and then bitching that they don't tell you cause.
Ipse dixit. Seems kind of arrogant to think that that observation doesn't have further implications that might hold some water. For instance that one might argue "[heights of six feet and more], it's a more of a guy thing". While that graph of mine, and Pinker's exposition are maybe a little vague, maybe the following modification might clarify things:
http://i62.tinypic.com/igvrxv.jpg
Which is saying that 2.275% of the female population is taller than 185 cm [about 73 inches] while 15.861% of the male population is taller than 185 cm. Which again justifies the claim that "[taller than 185 cm], it's more of a guy thing". But the graph can also be interpreted as saying that 2.275% of the female population is taller than 84.139% of the male population. All of which might reasonably be applied to questions of innate abilities such as reading and mathematics, although it might be emphasized or suggested that those abilities are not necessarily straitjackets: that women, as a class, might be better readers is hardly justification for any man to give up on the process.