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 formula 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"