Ah, I think I'm with you now. My stats is rusty, but I think what you're asking about is one of the fundamentals of variance.
I think this[1] Stats StackExchange answer frames it well.
[1]: http://stats.stackexchange.com/questions/129885/why-does-inc...
Re:Dutch men confirmed as world's tallest
by SideburnsOfDoom on Tuesday July 26, 2016 @07:34AM
(#12164846)
That is helpful, thanks. Especially this part:
> I believe that the Law of Large Numbers explains why the variance (standard error) goes down when the sample size increases. https://en.wikipedia.org/wiki/Law_of_large_numbers
So what I was looking at is the inverse of the law of large numbers.
1) https://en.wikipedia.org/wiki/Maxima_and_minima