Submitted by bookposting5 t3_109v749 in askscience
nog642 t1_j46jz9m wrote
Not sure about this specific case, but in general for this sort of thing (more difference between groups than within them):
Think of like a venn diagram with a large overlap. The difference between the groups is the distance between the two centers of the circles. The difference within the groups is the diameter of the circles. You can see how the former can be smaller than the latter, easily.
More accurately (and more mathy), think of two bell curves. The difference between the groups is the distance between the center of the two bell curves. The difference within the groups is proportional to the standard deviation or variance (4 standard deviations or whatever). Again you an imagine how by just putting the bell curves close together, they can remain clearly distinct while also having more difference within them than between the averages.
For an example more related to this, if you pick a trait like height for example. The difference in average height between people in your town vs the next town over (pretend you live in a town if you don't) is probably smaller than the difference in height between you and your sibling (pretend you have a same-sex sibling), despite the fact you are more closely related to your sibling.
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