Consider the 4 men on Mount Rushmore. Now let's average up their accomplishments (don't ask me how, just do it). At least one of them and possibly as many as 3 could have accomplishments which were less than the average for the group. Ergo, according to some people's logic, those guys must really suck.
Well yeah, that's exaggerated a bit, but it's what's behind expressions like "50% the (doctors, lawyers, engineers,...) are from the bottom half of their class". Strictly speaking it's true, and in some contexts might even be clever. But mathematically it's thoroughly asinine - it conveys no information that's meaningful about the performance of the affected individuals. Similar logic would lead you to conclusions like 50% of the decathlon finalists in the Olympics are inferior athletes, or that 50% of the serial killers are better than average citizens, or maybe that the winners of corresponding events at the Olympics and the Special Olympics had comparable performances. The obvious error in all of the above cases is that the populations being considered were from very narrow classes.
This article from The New Yorker by Atul Gawande has been widely discussed lately. In it the author discusses how not all doctors and clinics perform equally well by various yardsticks, using cystic fibrosis treatment as an example.
I don't have time to write any more about it right now, but it's worth a read. More later.