Are your friends more popular than you are? There doesn’t seem to be any obvious reason to suppose this is true, but it probably is. We are all more likely to become friends with someone who has a lot of friends than we are to befriend someone with few friends. It’s not that we avoid those with few friends; rather it’s more probable that we will be among a popular person’s friends simply because he or she has a larger number of them.
This simple realization is relevant not only to real-life friends but also to social media. In Twitter, for example, it gives rise to what might be called the follower paradox: most people have fewer followers than their followers do. Before you resolve to become more scintillating, remember that most people are in similar, sparsely populated boats.
The number of friends we have is typical of many situations in which the average deviates from individuals’ experience. Another is class size. Let’s imagine a small department offering three courses for the semester. One is a survey course with 80 students, one an upper-level course with 15 students, and one a seminar with five students. Now what is the average class size? Clearly, it is (80 + 15 + 5)/3, or 33.3 students. This is the number the department is likely to publicize.
But once again, let’s adopt the perspective of the average person and reexamine these numbers. Eighty of the 100 students find themselves in a class with 80 students, 15 find themselves in a class of 15 students, and five in a class of five students. Thus, the average student’s class size is (80 × 80 + 15 × 15 + 5 × 5)/100, or 66.5 students. This number is less likely to be publicized by the department.
Of course, the argument applies to many situations. Consider population density. The average number of human beings per square mile of the earth’s land surface is low. Looked at from the perspective of the average human being, however, the density is much higher because most humans reside in cities. Thus, we can conclude that despite being more crowded together than average, most of us are less popular than average.