That's because you need to know that there are ~20 million veterans and ~1.87 million elementary school teachers, i.e. you need to know the base rate if I'm reversing the calculations properly.
Another flaw of averages is apparent when you realize that the average person has less than two eyes.
That must mean that well over 10% of adult male (from the other statistic that 90% of veterans are male) Americans have served in the military. I never would have thought the number was that high, especially with the military being all volunteer for decades.
There are about 2mm active and reserve military members and about 400mm Americans on the whole, so there are, at any time, 0.5% Americans in the military. Assuming the average enlistment is 1 term or 4 years, and people have about 80 year lifespans, then you get ~20 (80/4) "generations" of enlistments over a person's lifespan. 20 * 0.5% is 10%, so about what you would expect for "living veterans" if you had a constant cycle of veterans through the system. That's serious back of the napkin math (lots of assumptions!), so it might be incorrect, but I think it shows that 10% isn't too far from what you might expect, right?
Possibly, though I would think that many who serve do more than 1 enlistment. It's just that from my own personal experiences I've encountered few veterans in my life (except for older generation family members who served in WWII), that's why intuitively I find the number a bit surprising.
Yes, it should be median though the original is true for symmetric distributions. If you apply the central limit theorem, then you could say that half of all randomly samplings of a population are, on average, dumber than the population's average.
Since intelligence must be a one-sided distribution it's probably right-tailed, which means the mean is higher than the median. So I expect (slightly) more than half of the population to be dumber than average.
Those are all small, independent random contributions that naively would lead to a normal distribution per the central limit theorem. But it can't be quite a normal distribution due to the lower bound of 0 (in terms of absolute intelligence, not IQ). A better candidate would be a log-normal distribution which is always right-skewed.
Exactly half under is correct only for if none is exactly at the median, which requires (but is not necessarily the case when) there are an even number of measures.
Another flaw of averages is apparent when you realize that the average person has less than two eyes.