# Is there a way to estimate the distribution from only a small number of outliers?

For example, I was looking at this list of the 93 people who have broken the "10-second-barrier", after reading that sprinter Christophe Lemaitre was the first person of purely European decent to break the barrier, which got me to wondering what the difference between the mean sprinting times for whites vs blacks. Unfortunately, that number is probably not known since it would require making thousands of average people sprint, and even then it wouldn't necessarily reflect the "true genetic" difference, since the people sprinting were not training for sprinting. So if you wanted to measure the genetic component of the difference, it might be more accurate to measure only the fastest people in the world who are equally motivated and have been training for years, and therefore have eliminated the non-genetic disadvantages, at least that would be my theory.

So if you could get a list of say the top 1000 fastest times in the 100 meter dash, and say 20 people on that list are white, could you use that data to give some estimation on what the full distributions look like and/or find what the mean of those distributions are? How?

QUESTION is above^^ this is just some rambling:

I would guess that if you were trying to find the difference in means between blacks and whites 100 meter sprinting times AFTER everyone in each population had trained for years, lost excess weight ect, i.e. you only want to measure the genetic difference in maximum potential, then measuring average people will not be the way to go, since none of them will have trained to reach their maximum potential, thus there will be many non-genetic factors causing differences, and the other problem is that the difference between trained and untrained, may not be the same, so if you want to measure difference in max potential, it would be better to look at the 1000 fastest, rather than 1000 average people. Also, the data for the 1000 fastest is very high quality, since it was done with laser timing and under official supervision, whereas data gathered from some fitness survey done at a few high schools would probably be of low quality.

I have strong reservations about whether mean white sprinting time vs mean black sprinting time is even possibly a meaningful question. But setting that aside, no you won't be able to do this from the top 10. Even assuming the data are normal (which I also doubt), take as an analogy the distributions of IQs for men vs women. It is generally held by people who study such things that the distribution of IQs is normal and is standardized to mean $100$ & SD $15$. As you move further up, the ratio of men to women increases, but this is because the SD for men is $15.5$ vs $14.5$ for women. Nonetheless, the mean for women is considered to be $100.5$ vs $99.5$ for men.