Why over a half?
Exactly half of people are at or below average intelligence - by the definition of an arithmetic mean. So why over a half? That confusing message has been caused by you including the condition 'of people you meet.'
That depends who you meet. If you are a university professor, slightly over half the people you meet may be of over average intelligence. If you are in prison, over half the people you meet are likely to be under average intelligence.
Your clever statement - which went slightly awry - would be better stated 'half of people are of average intelligence or below.'
Well, these are all hypothetical statistics, seeing as none of us truly "meet" a sterilized, clinical sample of human beings so as to be representative of all levels of cognative ability in any given day, or even in a lifetime, but it does depend on where you are taking your average from. Please refer to this abitrary, unfounded graph of real-legit scientific data showing the bell-curve of the inteligence of the human race:
as you can see, only a small portion of people are geniuses, while most are genuinely close together. so if we take our "average" as meaning the top 50% and the bottom 50% of humanity (which if I'm not wrong is called a "median" and not an "average"), statistically you will meet just as many sub-par beings as you will outstanding ones- however, if we state that our definition of "average" is rather the halfway point between top of what can be possibly achieved but the most absolutely stellar god-tier pc-elitist human beings, and some sort of absolute baseline, which we will arbitrarily call the point of brain death, a larger-than-50% portion of our random survey people will be below average. Science!
Wow. that was so arbitrary and not peer reviewed or backed by any meaningful research or consensus. I can't believe that I felt that that was an appropriate reply. seriously, I made a curve chart in paint with three colours at 3am to defend a moot point on an internet forum that is without any doubt completely unrelated. I must be tired. time to stop.