"Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost." -- (W. S. Anglin) Perfect numbers: Euclid (ca. 300 B.C.) defined a perfect number to be a number that is "equal to the sum of its parts." That is, a number is perfect if is the sum of its proper divisors (all divisors except the number itself. The smallest perfect number is 6 = 1 + 2 + 3. The next perfect number after 6 is 28 = 1 + 2 + 4 + 7 + 14. Perfect numbers are few and far between, and to this day, there are unsolved problems relating to these numbers. For instance, no odd perfect number has ever been found - and no one has been able to prove there aren't any. Finally, here is a mind-boggling fact. Of the eight smallest perfect numbers, the largest is 2,305,843,008,139,952,128 What did Herkimer call the monk who was selling potato chips? Answer: A chipmunk Herky's friends: HUGH MORRIS...this guy is the funniest of Herky's friends. MARY SCHINO...she sells those red cherries that one puts in certain alcoholic drinks. ASSIGNMENT #57 Reading: Chapter Review (pages 495-497). Review Chapter 9, as necessary. Exercises: Page 494/9.36, 9.37, 9.38, 9.39. Do these on a separate piece of paper. Write them up neatly. Communicate as you will have to do on the actual AP Stat. Exam. You are working with concepts from Chapter9.

Make sure that you understand the Central Limit Theorem. Basically, you have a population with mean m and standard deviations. Thepopulation itself does not have to have a normal distribution. Consider all random samples of size n, and let M be the set of allsample means. The Central Limit Theorem tells you something aboutthe set M (not the population itself). If n is large, the samplingdistribution of M is approximately normal with mean m and standarddeviation s/n.

The mean of sample means from samples of size n isan unbiased statistic. That is, the mean of all the sample means is the is equalto the mean of the population. A samplemean is an unbiased estimator of the population mean (aparameter).

The standard deviation of a sample mean is not anunbiased statistic. The mean of all sample standard deviations isnot the standard deviation of the population. In a nutshell,a sample standard deviation would not be agood estimator of the population standard deviation (aparameter).

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Text:
The Practice of Statistics, by Yates, Moore, McCabe. New York,W.H. Freeman and Company, 1999. (ISBN 0-7167-3370-6)

Supplemental books:
The Cartoon Guide to Statistics, by Gonick and Smith. NewYork, HarperCollins Publishers, 1993. (ISBN 0-06-273102-5)
How to Lie with Statistics, by Darrell Huff. New York, W.W.Norton & Company, 1982 (ISBN 0-393-09426-X)