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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 \(\mathrm{b}\) equal? If not, why not?

Step by step solution

01

Calculate the mean size of the 25 classes

To find the mean size of the 25 classes, take the total number of students and divide by the number of classes. There are 600 students in 24 classes of 25 each plus 150 students in one class, for a total of 750 students. The number of classes is \(4*6+1=25\). So the mean size is \(750/25 = 30\) students per class.

02

Calculate the mean class size from a student's perspective

Each student is enrolled in five classes. In four of those classes, there are 25 students, and in one class, there are 150 students. So, to a student's perspective, the average class size is \((4*25+150)/5 = 50\) students per class.

03

Compare the two means

The mean class size from the university's perspective is 30 students per class, and the mean class size from a student's perspective is 50 students per class. The means are not the same because they're being calculated with respect to different populations. From the university's point of view, each of the 25 classes is an individual unit, while for a student, the unit is their personal list of five classes.

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