Statistics Formula: Where did it come from?

Main Question or Discussion Point

Hi, I have just started my AP Stats class and we have a short quiz tomorrow on a few things. I was just wondering where did this http://math.sierra.cc.ca.us/Statistics/statisticsformulas/statis3.gif come from? Where did those numbers come from to create that forumula?
 
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Answers and Replies

mathman
Science Advisor
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This may not answer your question completely. However the mathematical expectation (theoretical average) of s2 is the theoretical variance of the statistical average.
 
lurflurf
Homework Helper
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This will not be completely answer it but
In statistics the idea is to get a picture of how lots of numbers act by using a few numbers. The first statistic often used is the mean
mean=sum/number
If our data has mean 0 we might like to know are all the numbers zero, most, maybe half are 1000000000 and half -1000000000. We want an idea of spreadoutness. so we consider
mean(x-mean(x))
but it is zero we cure that with
mean((x-mean(x))^2)
but we are using n numbers like n+1 (mean(x) depends on x hence is not its own number)
so we do
(n/(n-1))mean((x-mean(x))^2)
but it is squarey so
sqrt((n/(n-1))mean((x-mean(x))^2))
which is the standard deviation we know and love
 
That helps thx. I now get most of the formula except why is it (n-1)?
 

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