It's not, because the number of children with IQ >= 130 from a certain group depends on the average IQ of children in the group. If the average IQ of children of college gradutes is 115, a much higher fraction of them will be gifted than the children of parents who did not go beyond high school. In other words, the entire distribution of IQ in some groups is shifted toward the right, and in other groups shifted toward the left, which has implications for the incidence of giftedness.
This argument is a solid demonstration of innumeracy. Whether the gifted population in your sample is 1 in 50 or, let's say, 1 in 10, the group still isn't large enough to significantly influence averages.
.
I think the argument is correct. If variables X and Y are drawn from normal distributions with SD = 15, but the E[X] = 115 and E[Y] = 100, there is a much higher probability that X >= 130 than that Y >= 130.
If you define "very tall" as a height of 6ft 6in or more, there are many more very tall men than women because men are taller and their distribution of heights is shifted to the right relative to the distribution of female heights. Do you think the children of parents who both dropped out of high school are as smart on average as the children of parents who both earned college degrees? Unless you do, you should not be surprised if a smaller fraction of the former group than the latter one have IQs >= 130.
