I have the following problem that I'm having great difficulty solving:
One group of students (sample size a) scored an average of b on an exam. The standard deviation of these results was c. Another group of students (sample size x) scored an average of y in the same exam, with a standard deviation of z. What is the mean and the standard deviation of the two groups of students as a whole?
I know that the weighted mean is given by (a.b+x.y)/(a+x); but I have no idea how to get the weighted standard deviation. Any ideas?