Date:         Fri, 27 Apr 2007 16:53:32 -0400
Reply-To:     "Wainwright, Andrea" <andrea.wainwright@CAPITALONE.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         "Wainwright, Andrea" <andrea.wainwright@CAPITALONE.COM>
Subject:      Re: Central Limit Theorem
Comments: To: Peter Flom <peterflomconsulting@mindspring.com>
In-Reply-To:  A<13044437.1177706923759.JavaMail.root@mswamui-blood.atl.sa.earthlink.net>
Content-Type: text/plain; charset="us-ascii"

In reading the original I had the same response you did.

The distribution of the mean from multiple samples will be approximately
normal, but any given sample can't be assured to be normally
distributed.

-----Original Message-----
From: SAS(r) Discussion [mailto:SAS-L@LISTSERV.UGA.EDU] On Behalf Of
Peter Flom
Sent: Friday, April 27, 2007 4:49 PM
To: SAS-L@LISTSERV.UGA.EDU
Subject: Central Limit Theorem

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



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