- Thread starter
- #1

Any help with this one would be appreciated.

In a college 80 students are taking the exam in the spring semester. Their grades has a mean and standard deviation.

In the summer semester, k additional students are being tested. All k students get grades which are equal to the average grade of the 80 students from the spring semester. After combining both samples, we get a standard deviation which is half of the standard deviation of the first 80 students. Find k.

I did something, and got k=80, but I am not sure it's correct, would appreciate if anyone can validate my answer.

what I did was to take S1 (the standard deviation before any addition) and I said it is equal to 2*S2 (which is the standard deviation of the two samples together).

Then I realized, that since all observations in the second sample are equal to the mean, than the numerator is equal in both parts of the equations (apart from the 2 of course). Moreover, the sums of deviance are equal.

Then I solved the equation to get k=80

P.S In this context, when I say variance I mean the formula in which we divide by n, not by n-1.