Will Rogers allegedly 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.