# Statistics Formula: Where did it come from?

by Learning Curve
Tags: formula, statistics
 P: 117 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 formula come from? Where did those numbers come from to create that forumula?
 Sci Advisor P: 5,767 This may not answer your question completely. However the mathematical expectation (theoretical average) of s2 is the theoretical variance of the statistical average.
 HW Helper P: 2,078 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
P: 117

## Statistics Formula: Where did it come from?

That helps thx. I now get most of the formula except why is it (n-1)?
 P: 24 http://en.wikipedia.org/wiki/Variance Read the section "Population variance and sample variance"

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