Suppose that there are 150 freshmen engineering majors at a college and each of them will take the same five courses next semester. Four of these courses will be taught in small sections of 25 students each, whereas the fifth course will be taught in one section containing all 150 freshmen. To accommodate all 150 students, there must be six sections of each of the four courses taught in 25-student sections. Thus, there are 24 classes of 25 students each and one class of 150 students.
a. Find the mean size of these 25 classes.
b. Find the mean class size from a student’s point of view, noting that each student has five classes containing 25, 25, 25, 25, and 150 students, respectively.
Are the means in parts a and b equal? If not, why not?