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# CLASS 11

## HANDOUTS:

(1) News articles from Orlando Sentinel and Courier-News on SAT exams. (2) SAT Coaching by Fredrick L. Smyth, (3) Sex bias and the scholastic aptitude test by Morgen Sullivan.

## DISCUSSION

Read the two news articles about the SAT exams and discuss the following questions:

1. How much would you design an experiment to settle once and for all how much coaching helps students SAT scores on the average?

2. What do you think the SAT examinations measure?

3. Women do less well on SAT exams and as well or better in their performance in college. Why do you think this is?

4. Do you think that too much emphasis is placed on SAT examinations in admission to college?

## JOURNAL ASSIGNMENTS

(1) SHUFFLING

Include in your journal the solution to the following two problems that John Finn provided as a help to understanding shuffling. He will give part 2 of his account of shuffling next Tuesday.

1) Find the Pythagorean distance between the uniform density on permutations, and the one you get by doing a single duffle, to a deck of 4 cards.

2) If you look at the first page of my shuffling outline, you'll see that a shuffle of 10 cards is uniquely determined by a list like 1011010110 of 0's and 1's. Assuming that these shuffles are all equally likely (which does turn out to be true, as we'll see next time), you should be able to figure out the density on permutations of 10 that you get by a single shuffle. You can't be expected to work out exactly *which* permutations get which probabilities, but since we really only want to know how far this is from uniform, you only need to figure out *how many* permutations get which probabilities.

(2) SAT SCORES

We have put on public a folder called SAT that has data relating to Dartmouth. The Elliott Strenta study has information about SAT scores and performance in college. In addition we have grades for several Dartmouth courses in recent years. See if you think that the SAT scores underpredict the performance of women at Dartmouth? Do women do better than men in some courses and not others?

## PROJECT SUGGESTIONS

(1) SHUFFLING: See if you could explain why 7 shuffles suffice in such a way that your Uncle George or your roommate would understand. We have video tapes of John Finn's lectures that would help in this. If you succeed we will put your write-up on gopher for future students to enjoy.

(2) CLASS ATTENDANCE: There are many interesting questions that you can ask about students attendance of classes at Dartmouth. For example, it is not uncommon for a mathematics professor to notice that only about 60 to 70 percent of the students are in class on a given day. Does this proportion vary a lot from day to day? Does it depend on the size of the class? on the discipline? Does it vary a lot between students? What are the reasons for students not attending classes?

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laurie.snell@chance.dartmouth.edu