Which of the following values is unusual?

Question

The mean of a distribution is 10 and the standard deviation is 3.

 

6

3

10

16

Answer 1

This distribution could have few samples or many samples, but the average - or mean - result is 10. The standard deviation of 3 tells us that a little more than 2/3 of all samples fall within +/-3 of that mean, so most results are from 7 to 13 (10-3 & 10+3). We call this the 1st standard deviation. The 2nd standard deviation covers an additional 28% or so of data - half of it below the mean & half of it above the mean. Again, the standard deviation being 3 tells us that it covers data 3 more below & above the mean - or 4 to 6 & 14 to 16. The 3rd standard deviation, then, are much rarer cases: 1 through 3 & 17 through 19. Obviously, 10 is among the most common examples in this distribution, while 6 & 16 are within the 2nd standard deviation. 3, however, is much rarer, being beyond the 2nd standard deviation.