Don’t miss Bryan Caplan’s clear and important explanation  of how averages can be very misleading.
Bryan’s post reminds me of an argument that I encountered years ago – I forget now who made it – about immigrants and education. The argument was that immigrants reduce the average level of education in the U.S. The clear point of this argument was to bolster the case against immigration. A lower average level of education, after all, is worse than a higher average level of education. Immigration’s negative effect on the average level of education in the U.S., it was implied, is a cost of immigration.
But clearly, although an illiterate and totally uneducated immigrant who moves to the U.S. does lower the average level of education among people living in the U.S., this immigrant does nothing to any individual’s level of education. I retain my PhD and all the knowledge that I accumulated over the years.
I use average height to explain to my students the problem with taking averages at face value. Suppose the average height of my class of 200 students is calculated and turns out to be 5’8”. Then let Yao Ming  walk into the classroom. Because he is 7’6” tall, he will increase the average height of people in the classroom – but do nothing to the heights of any individual in the classroom.