Question

There are two calculus classes at your school classes have a class average of 75.5 the first class as a standard deviation of 10.2 and the second has a standard deviation of 22.5 how do the classes compare

Answer 1

To compare the two classes, the Coefficient of Variation (COV) can be used.

The formula for COV is this:
C = s / x

where s is the standard deviation and x is the mean

For the first class:
C1 = 10.2 / 75.5
C1 = 0.1351 (13.51%)

For the second class:
C2 = 22.5 / 75.5
C2 = 0.2980 (29.80%)

The COV is a test of homogeneity. Looking at the values, the first class has more students having a grade closer to the average than the second class.