The idea that 50% of the constituent members of any group will naturally and logically be above average and 50% below it is not based on general realities. The facts don’t support it but rather show it to be mainly wishful thinking or at best, flawed reasoning. And all one has to do to test such a theory is to look at practically any large sample group and see that life doesn’t tend to fall into neat bell curves, let alone clean divides between the Half Above and the Half Below.
If it were true, for example, the high proportion of car drivers claiming to be above average in skill couldn’t possible be right, but of course we all know that drivers could never, ever have delusions of adequacy. We humans are not at all inclined to exaggerate our prowess and assume we are superior to the majority of others. Cough, cough.
Fortunately for you out there, I am one of those rare creatures whose positive self image does not hinge in any way upon my skill as a driver, which I believe in turn is what allows me to tell you without shame that I think I’m probably below average in that regard. Also fortunate for you is that I don’t drive a lot, which I suspect explains my having achieved this great old age without having been stopped by the police at any time. That, along with having something above the average level of being Lucky. Maybe this is how the universe maintains its balance, after all. I’m not opposed to hanging around both sides of the fence from time to time.
If you’ll let Mr. Mathman make an emendation: it’s the median, not the average (also called the mean), that is the value such that half the scores lie below it and half above. (It’s a little more complicated than that, but we needn’t get too detailed here.) Unlike the median, the average is susceptible to undue influence from atypical scores. For example, if the scores are 0, 0, 0, 0, 0, 6, the average of those six numbers is 1, but five of the six scores are below the value of 1.
I stand corrected. Right here in the median!