Freedman's paradox

Freedman's paradox is like a puzzle. It's a problem in statistics that is very tricky to solve. Imagine that you have a group of people who are all the same age. You want to know whether one group of people is taller than the other. So you measure each person in the group and you find out that the average height of the first group is taller than the average height of the second group. But when you look at each person in the group one by one, you find that some of the people in the second group are actually taller than some of the people in the first group! This seems like it doesn't make sense, but it happens sometimes in statistics. This is Freedman's paradox.