The Maths of Popularity

This sort of plays into a social phenomenon I've noticed. I've talked to highschool friend and told them that I always felt that they where more "in" with our group and I was a little more "out" with our group. They swear that I was one of the central figures in our group, and they where more of the outer shell. I've talked to others that I didn't even know in highschool, and many people I know seem to have had this perception about their circle.
It may just be indicative of the people I am likely to associate myself with, but it could also be that the laws of statistics play against our own insecurities.

This is the same effect that leads to the following (seeming) paradox:

Imagine a small school with 40 students each taking 5 classes. Thirty of them are in classes together as a group. These 5 classes have an average class size of 30 students. The other 10 students are in their own separate block of 5 classes. This second set of five classes has an average class size of 10 students. The school sees 5 classes of 30 and 5 classes of 10 and claims an average class size of 20 students. But the students see something different. 30 of them see an average class size of 30 and 10 of them see an average class size of 10. Thirty 30's and ten 10's average to 25. So, from the students' perspective, the average class size is 25. This was simplified, but it's the general way that this works in any school with any number of students.

It is an interesting effect (and shows that averages are not as intuitive as we think they are).