standard deviation and N-1

From: Victoria Florsheim (vf2_at_buffalo.edu)
Date: 07/08/04 

Date: Wed, 7 Jul 2004 21:50:45 -0400

In high school, I learned that the formula for standard deviation has n in
the denominator, but in college the book has N-1 in the denominator. What
is the reason for this?

So far, I found this in my book (By Yates, Moore, McCabe):
Why do we average by dividing by n-1 rather than n? Because the sum of
deviations is always zero, the last deviation can be found once we know
the other n-1. So we are not averaging n unrelated numbers. Only n-1 of
the squared deviations can cary freely, and we average by dividing by the
total by n-1. The n-1 is called the degrees of freedom of the variance or
standard deviation.

I sort of understand that, but could someone explain in simpler terms and
expand on that? I'm still a little puzzled as to why n-1.

Thanks.

Relevant Pages

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