Facebook reports that the average number of Facebook friends worldwide is 175.5 with a standard deviation of 90.57. If you were to take a sample of 25 students,

Question

Facebook reports that the average number of Facebook friends worldwide is 175.5 with a standard deviation of 90.57. If you were to take a sample of 25 students, what is the probability that the mean number Facebook friends in the sample will be 190 friends or more?

Answer 1

Mary,

This is an interesting problem, but not necessarily only from the statistical point of view! As statistics, you look for the probability for n=25 that the number of Facebook friends is at or exceeds 190. Since the expected sample deviation of this sample scales with (n-1)^0.5, you could proceed by calculating 90.57/(24)^0.5 (that's the sample deviation of averaged samples of 25 students), and then looking up probability for the occurrence of deviation of (190-175.5)= 14.5 vs. this sample deviation.

But that's not the interesting part! When Facebook says worldwide, I bet you they mean, among FACEBOOK USERS. So when you take 25 students at random worldwide, what proportion of them will be on Facebook...? AND, do students (in general) tend to have more or less Facebook friends than do all Facebook users? Neither of these factors can be neglected, and there may be others I haven't even thought of yet.

Right away, you can see that there are major problems with the way that this question has been posed.

Why not shoot it out there onto Facebook, and see how many of your 175 Friends respond helpfully (and heaven help you if you're already trying to wade through thousands of daily postings!).

Cheers --

S. de Riel