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?
1. Read the article about the work of Tversky and Kahnenam from Discover magazine, Vol.6, No.6, June 1985.
2. Choose a stock or a baseball player or some other data that you can think might have streaks and see if it can be considered to have a streak behavior significantly different from a coin tossing process. (possibly a biased coin). The stock market and baseball data will be on public and on gopher.
David Gonzalez said that at first he felt ``if you're scared of the possibility of EMF danger, take adequate precaution." However he ``soon realized that the heart of the debate is a public policy perspective that involves people who don't have the option of just moving their home because a power line is overhead."
Although most people found the article on smoking and lung cancer very persuasive, several people were critical of surveys as a means of gathering reliable information. Some found other weaknesses in the study, like Lee Grinberg who thought ``the study neglected any effect that pollutants in the air may have had on the patients..."
Steve Murphy had questions about the ``pennies" experiment and wondered if ``so many people are doing an experiment, the method can never be absolutely consistent" across all participants.
Many people are surprised by some of the results from our class survey. Juan Serrano writes, ``I thought more people would drink coffee because of the need to stay up nights to do Math 5 work."
Amy Peller was interested in the way statistics can be used to persuade people. She commented that ``It is frightening that the people devising and quoting statistics have the power to either intentionally or unintentionally mislead others." She also notes that ``this is a power which can easily be abused seeing that many people are generally willing to accept any sort of information as long as it is backed up by numbers."