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February 18th, 2009, 06:57 PM   #1
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weight of variances in 2 values on overall variance


I've been having a heck of a time today trying to find the answer to this question. If you have variances in 2 values which are contributing to an overall variance, how do you determine the percentage of the overall variance the variance in each value comprises? For example....

If I expect to see 300 clients in 100 staff hours per week, I have a target efficiency of 3 clients/staff hour. However, in one particular week I see only 250 clients with 125 staff hours. My efficiency for this period is only 2 clients/staff hour. My overall efficiency is down 33% to target. My clients are down 16.67% and my staff hours are over by 25%. How do I determine what percentage of the 33% decrease in efficiency is attributable to increased staff hours and which is attributable to decreased clients?

It seemed like a simple thing until I tried to sit down and figure it out, and I'm sure it's encountered all the time in looking at efficiency numbers in all kinds of business applications, but for the life of me I just can't figure out the formula to use to determine this. I'm hoping someone here can help me out. Thank you in advance for your assistance.

Edit: Found a solution today. In the example above, 16.67x + 25x = 33, x=33/41.67, x=.7919, 13.2 + 19.8 = 33, 13.2/33 = 40% & 19.8/33 = 60%
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values, variance, variances, weight

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