# Measures of Central Tendency and Dispersion

## Mean, median, mode, range

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Popularity

Credit: Ahmed Mando
Source: http://www.flickr.com/photos/51788543@N00/199178572/

Ever feel like you’re not as popular as your friends? Or that they are friends with more people than you are? Well, statistically speaking, this is quite natural. This is the case for most people. So you’re not really unpopularyou’re actually the majority!

#### How Does It Happen?

Let’s illustrate this phenomenon with an example. Consider a closed group of 5 people: Kim, Khloe, Kourtney, Kendall, and Kylie. Khloe is friends with Kourtney, and Kendall is friends with Kylie. Kim is friends with all the others.

Credit: Bill Chance
Source: http://www.flickr.com/photos/chancew1/8614705885/

The total number of friends Kim has is 4, but the others each have 2 friends only. The average number of friends Kim's friends have is 2, which is less than Kim’s own number, making her "popular." But the average number of friends Khloe’s friends have is \begin{align*}\left ( 4+2+2+2\right )/4=2.5\end{align*}, which is higher than Khloe's own number. The same is true for Kourtney, Kendall, and Kylie as well. So the statement, “My friends have more friends than I do,” is actually true for 4 of these people, Kim being the only exception. This same principle applies to Facebook friends, Twitter followers, and to the hypothesis: “People I’ve dated have dated more people than I have.”

You can find a more detailed analysis here: http://www.economist.com/blogs/economist-explains/2013/04/economist-explains-why-friends-more-popular-paradox

#### Explore More

Try verifying this with your friends. Pick a group of people on which to run the experiment; it can be all the students in your class or some random people on Facebook. For each person, calculate the average number of friends his or her friends have and compare it to the number of friends that person has. See how many times the former is higher than the latter.

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