In season 6 episode 8, Sheldon says that, statistically speaking, Leonard should worry about Penny’s friend.
Well, if we assume your looks are average, yeah, right off the bat, fifty percent of men on Earth are more attractive than you. That’s one point five billion handsome lads standing by, waiting to rain on your parade.
Sheldon assumes that if Leonard’s appearance is average, 50 percent of men are more attractive than him. He makes the classic statistics mistake by confounding the average (mean) and the median. Leonard being “average” does not define his location on a scale of appearance. Average ≠ middle.
For example, in Fig. a,
the red bars represents members of the male population who are less attractive than Leonard. The blue bars represent members of the population who are more attractive. As you can see, Leonard is the exact average, being in the middle. This is an idealized situation where Sheldon would be correct (because there are 9 less attractive and 9 more attractive).
However, consider Fig. b,
In this example, there are 16 men less attractive than Leonard and 2 men more attractive. Yet, Leonard is still in the average. Despite being in the average, he is not in the middle, with 11% of men more attractive than him.