Mrs. Hopkins has two math classes, each with the same number

I think it is E.

The only inference from the stem is that the total mean of the two classes is the average of the two means. Unless we have some kind of relationship about the marks, it is tough to determine individual means from either (1) or (2) or combined and thus the total deviation.

SD = sqrt(sum of squares of the mean deviations/total number of samples)

What we need to find out is the mean of all the students of both the classes and then compute the SD. By the very nature of the above formula(sqrt) and the statistics(two same groups may have different means but their mean deviations sum might be the same), we cannot say that SD = SD1+SD2 or anything of that kind.

OA please..

Yup, you're all right! It is E. And the various explanations are all right.

For this question, you need to know that standard deviation alone means nothing without the average it's describing. If the test scores' SD was 2 for both classes, we don't know if they each averaged 85, or if one class averaged 80 while the other averaged 90. Without information about the actual test grades of the various students, we can't know what the standard deviation is.

Bottom line, you can't do anything with SD except describe the average. You certainly can't combine different ones in any meaningful way.