Date:         Fri, 27 Apr 2007 16:48:43 -0400
Reply-To:     Peter Flom <peterflomconsulting@mindspring.com>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Peter Flom <peterflomconsulting@MINDSPRING.COM>
Subject:      Central Limit Theorem
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I am reviewing and editing a statistics book.

In it, they have the following statement re the central limit theorem

"Regardless of the shape of the population, if a sufficiently large random sample of size n is taken from the population, then the sample is approximately normally distributed, with mean mu sub xbar and standard deviation sigma/sqrt(n)"


????

This seems completely wrong!

The CLM is not about ONE sample, but about MANY samples.  That is, it should be

"Regardless of the shape of the population, if a sufficiently large NUMBER of samples of a particular size is taken, then the distribution of the mean of the SAMPLES approaches normal as the NUMBER of samples approaches infinity"

I googled a bit, and did not find a really good clear statement of this - the book is intended for HS students.

Anyone got any suggestions? Am I all wrong? Is the author all wrong? Are we BOTH wrong?

Happy weekend!

Peter