Statistics Formula: Where did it come from?

[Learning Curve]

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?

 

[mathman]

This may not answer your question completely. However the mathematical expectation (theoretical average) of s² is the theoretical variance of the statistical average.

 

[lurflurf]

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

 

[Learning Curve]

That helps thx. I now get most of the formula except why is it (n-1)?

 

[Zone Ranger]

http://en.wikipedia.org/wiki/Variance

Read the section "Population variance and sample variance"