"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)

Math History Tidbit:

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


Herkimer's Corner

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.


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.

Items for reflection:

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).





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)

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