Man, I hate posting on these Charles Murray threads as I am so easily out-gunned. But in this case, I have to say it, your definition describes the mean, not the average. You can work it out for yourself and I suggest you do, the difference is quite important.
I think it describes the median, which I believe is the most common understanding of "average" when it comes to demographics. I'm no statistician, but my understanding is that, if you take for instance the following set: 2,6,7,11,19
1. "Median" would be 7, with 2 and 6 below median and 11 and 14 above median
2. "Mean" would be 9, which is the sum divided by 5.
All that being said, I think I understand better the objection to what Murray said, now that its been explained. The IQ test is not accurate enough to know exactly who is average as opposed to a little above or a little below.
Still, I don't think Murray's point was that the measuring tool is necessarily precise, but that hypothetically, regardless of whether we can ACTUALLY DETERMINE who is above or below median, some are below average and some are above IN REALITY.