I'm sorry but when I first saw this question, I got totally thrown off, and it really confuses me. (I'm sorry because I know this should be really basic, and I'm not getting it..)

You have a sample of ten data elements (n=10). You accidentally compute a population standard deviation and find it equals two (2). What is the sample standard deviation?

I don't know why but the first thing that comes to mind when I saw this question was to use the Sigma/sqrt(n) formula to get the sample standard deviation. So I basically did 2/sqrt(10), and then of course that was wrong. But can you please tell me what is wrong by doing it this way because it is really messing up my concepts about population and sample variance. Thanks.

ANSWER:

The population variance = 2^2 = 4. This means sum of squared deviations = 4*10 = 40. Divide 40 by (n-1) to get the sample variance, which equals 4.44. So that sample standard deviation = SQRT(4.44) = 2.11. In short, sample variance = population variance * n/(n-1).

and also, I went over the 2008 quant notes and wasn't able to find the above formula.