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 Probability and Statistics
 Proof of Sample Variance Equation
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carolynt
New Member

USA
2 Posts

Posted - 09/25/2007 :  09:54:26  Show Profile
I have been trying to prove that one form of the equation for sample variance,x-((x)n) = (x-mean), another form of the same equation.

So far, given the definition of mean being xn , I now have x-((x)n) = (x-((x)n))

I have been looking online and have not found what to do after this step. Is there a way to separate the right half of the equation into the two parts separated by the subtraction on the left side? Or how can you change the n that is on the right side into the n present on the left?
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tkhunny
Advanced Member

USA
1001 Posts

Posted - 09/25/2007 :  10:40:42  Show Profile
It may help to know the specific words "Machine Formula".

http://www.bls.gov/ore/pdf/st990210.pdf
http://www.cba.uh.edu/peixoto/DISC6360/s_mean.PDF
http://faculty.washington.edu/conquest/482fall02/HW/hw1solution.htm

Also, please check your notation. You appear to have some exponents in the wrong places.
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carolynt
New Member

USA
2 Posts

Posted - 09/26/2007 :  06:37:54  Show Profile
You were right, the equation is x-((x)n)= (x-mean)

I finally found the proof. It is basically working with the principle that mean=(x)n. Also, that mean and x = nmean and nx, respectively. You can factor the (x-mean) into a trinomial, then, by reworking the two last factors using the definitions above, combine the second and third terms because they are like terms.

Thank you so much for your help and the website links!
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