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?
This may not answer your question completely. However the mathematical expectation (theoretical average) of s^{2} is the theoretical variance of the statistical average.
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