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My maths is a little rusty, but I understand how to calculate variance in general. A colleague asked me if I knew how to calculate the percentage variance on budget spending.

Given this example:

The first budget for a project was 5000 dollars, and the department spent 2500 dollars. The next budget was 5000 dollars again, but the department spent 6000 dollars. Calculate the variance percentage on spending.

How do I interpret this question, and will someone please give me a shove in the right direction?

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I don't think that is correct because I think the numerator should be a portion of the denominator. But you are using a center for the denominator of 5000 that is different from the center in the numerator 4500. So in theory you could have a quantity greater than 100%. – Michael Chernick Aug 24 '12 at 17:34
Thanks Michael, I showed my answer to my colleague and it coincided with his calculations, so he was satisfied. Unfortunately I do not have the time to dig deeper at this point. – Jack Dec 21 '12 at 8:54

Variance in spending (without considering budget):

Average spending = (2500+6000)/2 = 4250

Variance = ((2500-4250)^2)+(6000-4250)^2)/2
              = (3062500+ 3062500)/2
              = 153150

Variance against budget:

Variance = ((2500-5000)^2)+(6000-5000)^2)/2
             = (6250000+1000000)/2
             = 3625000

Percentage variance:

153150/3625000*100 = 42.24%
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