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Statistics Formula: Where did it come from?

by Learning Curve
Tags: formula, statistics
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Learning Curve
#1
Aug16-05, 03:12 PM
Learning Curve's Avatar
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?
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mathman
#2
Aug16-05, 04:30 PM
Sci Advisor
P: 6,106
This may not answer your question completely. However the mathematical expectation (theoretical average) of s2 is the theoretical variance of the statistical average.
lurflurf
#3
Aug16-05, 08:09 PM
HW Helper
P: 2,264
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
#4
Aug16-05, 08:41 PM
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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)?
Zone Ranger
#5
Aug16-05, 09:34 PM
P: 24
http://en.wikipedia.org/wiki/Variance

Read the section "Population variance and sample variance"


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