Will the mean equal the standard deviation

Question

In my problem, there are three classes that have each taken a test and in these classes, there are 99 students. Class A had 1 student who scored a 1, 1 students who scored a 99, and 97 students who scored a 50. In class B 49 students scored a 1, 49 students scored a 99 and 1 student scored a 50. In class C 1 student scored a 1, 1 student scored a 2, 1 student scored a 3 and so on until this class reached the 1 student who scored 99. The mean of all of these classes is 495 points and the range is equal as well. Does this mean the standard deviation is equal, too?

Answer 1

As you say, means and ranges (not shown below) are equal, for each of the three classes separately. (Also, for the aggregate of all three classes.) But the standard deviations are $not$ equal. The standard deviation is a 'more sensitive' measure of variability than is the range. Here are computations from R statistical software:

 a = c(1, 99, rep(50,97))            # quick ways
 b = c(50, rep(1,49), rep(99,49))    #  to represent
 c = 1:99                            #   your data

 mean(a);  mean(b);  mean(c);  mean(c(a,b,c))
 ## 50
 ## 50
 ## 50
 ## 50
 sd(a);  sd(b);  sd(c);  sd(c(a,b,c))
 ## 7               # least variation
 ## 49              # most variation
 ## 28.72281
 ## 32.92857

Using the hints in the Comments, you should be able to find the standard deviations using a calculator without much effort.