A good example of this is the genetic difference within Africa, which are larger, than the genetic differences between Africa and Europe.
From what I understand, on a mathematical level it means that if you take the averages of two groups and compare them to each other, the difference will be less, than the difference between the two extremes within a given group. This generally sounds logical. Since most people on earth are fairly similar, it makes sense that the average African is more similar to the average European, than the two most distant Africans compared to each other.
However, does this also mean, that two randomly selected Africans have a higher chance of being more different than a randomly selected European from a randomly selected African?
How is this law of variation between and within groups to be understood exactly? Does it still apply, when comparing the likelyhood of differnce between individuals, as opposed to the avarages or are those the same thing?
If we imagine a very simple example: two groups with 10 individuals, each assigned a value of 1 to 10.
First group has the values: 1,2,3,4,5,6,7,8,9,10 Second group has the values: 10,20,30,40,50,60,70,80,90,100
If you compare the averages you will get: 5 and 50, a difference of 45. If you compare the outliers within the second group you will get 10 and 100, a difference of 100.
If this is the case, than what exactly does it mean, that the differences between Africans are greater than between Africans and Europeans? Does it simply mean, that in Africa, there is a higher genetic variance? Does it mean that comparing any group to any other group is inherently useless, as the difference within the group is almost always going to be more significant, than the variance between the groups?