1. The problem statement, all variables and given/known data This is not homework. This is a question given in class with the answers already given. Neither the teacher nor the students have been able to figure out how to obtain the answers though, so my question is how to find them? Here is a picture of the question. The standard deviation, mean and variance are all for a population. None of them are for a sample, since it is not in the syllabus. The answer given is 492 for ∑f . x and 6114.1 for ∑f . x^2 2. Relevant equations The definition of the mean is: u = ∑(f . x)/∑f The definition of the standard deviation is: √v where is the variance, which is equal to: (∑(f. (x^2))/42 - u^2) Which is the mean of the square minus the square of the mean. 3. The attempt at a solution According to the definition of the mean, ∑f .x would be equal to 42u, since ∑f = 42. u = 72.3. This gives about 3036, which is obviously not equal to 492 Then, according to the definition of the variance, it is the square of the mean. Thus the square of 34.1 should be equal to ∑(f . (x^2)) - u^2/42. Thus: 42 * (34.1^2 + u^2) = ∑f . (x^2) Plugging in u = 72.3 gives 268384.2, which is again a far cry from 6114.1 So my question is, what is it that I'm doing wrong, and how to obtain the given answers? Thanks for any answers.