What does it mean for there to be more variance within groups than between groups in IQ? I was watching a short YouTube video that comments on the validity of IQ. That video contains the following claim (verbatim):


  "You know nothing about a person's intelligence on the basis of his or her skin color. That is just a fact. There is much more variance among individuals in any racial group than there is between groups..."


This was shortly after he stated that there are real differences in the average IQ of different races.

I find the bold statement confusing and am not certain how to interpret it. I understand what variance means when discussing a single probability distribution however, my learning never extended to variance between distributions. Could someone please explain how this is done and more importantly, why this measure justifies the first (non-bold) statement?
In the video he is discussing some work of Charles Murray (not sure how familiar you are with it). In any case, the main point of your confusion comes from the difference between presence and size. Dr. Harris admits that there are differential IQ values between the races: there is (presence) a difference. The immediate follow up, though, is that the size of that difference pales in comparison to the variability with the group, indicating that no practical conclusions can be made.

For a silly example (and not leave any Earth groups out), consider Martians and Plutons (poor Pluto...): Martians may have a slightly higher IQ than Plutons, but the variability within each group is much higher than the between group difference. Dr. Harris' whole point is that, upon meeting a random Pluton and a random Martian, you practically have no idea which of them will be smarter, even though we know that Martians tend to be smarter. A pretty picture illustrates the two groups below.

I hope this helps! Take home message from the video is that even though there are small differences between races in terms of IQ, they should not play a role in someone's judgement of another person due to the immensely higher variability of IQ within any given race (there are some super smart Plutons and some super dumb Plutons, just like there are some super smart Martians and some super dumb Martians: you won't know which you are speaking to until you actually talk to them).



Graph coded in R:

boxplot(cbind(Plutons = rnorm(1000, mean=100, sd=15), Martians = rnorm(1000, mean=102, sd=15)))