Will Rogers alleged said, "When the Okies left Oklahoma and moved to
California, they raised the average intelligence level in both states."
He was joking, but the effect is possible in principle. Consider two
sets:
A = {1, 2, 3, 4}
B = {5, 6, 7, 8, 9}
If we move 5 to set A, the mean of both sets increases.
This produces a somewhat paradoxical effect when doctors find a better way to
detect illness. Relatively healthy people are moved from the "well" category to
the "ill" category, and the average health of both populations improves even
before treatment takes place.
http://www.futilitycloset.com/2009/03/29/the-will-rogers-phonemenon
