Average class size

One of your friends at Harvard complains that the average class size at Harvard is too big. He bets that your average class size is much smaller. You decide to see if he is correct. Unfortunately, you are not sure how to measure average class size.

Your first idea is to see if the registrar will give you a list of all the classes this term and the size of each classes. Then you will just average these to get average-class-size-1.

But then you have another idea. ``I'm a rather typical student and taking three courses. Why don't I just take the average of the sizes of my courses?" Then you worry that perhaps you are not completely typical so you decide to ask a bunch of students to do this and take the average of their responses. Better yet, you ask the registrar to do this for every student and give you the average of all student averages. That surely should be what your friend would mean by the average class size. You call this average-class-size-2.

1. Would these two averages be the same? If not which will be bigger? Which would be more appropriate (a) for the President talking to Alumni (b) for the chairman of the mathematics department arguing for more appointments in> the math department?
   
   
2. You could have asked about the median class size instead of the mean. With either of these methods do you think that the median would be smaller or larger than the mean?
   
   
3. Make an estimate for both of these averages just using class size information from members of your group.
   
   
4. Do you have any other method to suggest for calculating average class size?
   

Homworks