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I calculate a project's change order rate by dividing the cost increase by the awarded value. For example, if the awarded value is 10,000 and there is a cost increase of 200, the change order rate would be 2% (200 / 10,000). The overall change order rate of a sample would be the sum of cost increases from all projects divided by the sum of awarded values for all projects (sum of all cost increases / sum of all awarded values).

My question: I want to calculate the overall standard deviation of change order rates. Can I divide the SD of the cost increases by the SD of all awarded values (SD cost increases / SD awarded value) and report this as the standard deviation of change order rates?

See example: Example

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No. You can check it yourself. For example, the standard deviation of change order rate (2%, 21%, 33%, 5%) is 14.5%, which is different from your 56%.

In other words, your question is whether the standard deviation of a ratio distribution (https://en.wikipedia.org/wiki/Ratio_distribution) equals the ratio of standard deviations of the two distributions. The answer is no. Even the mean of a ration is not equal to the ratio of mean values of the two distributions. Actually, the analytical solution to the standard deviation of a ratio distribution is quite complex. For example, the ratio of two normals with mean zero is Cauchy (https://en.wikipedia.org/wiki/Cauchy_distribution), while the mean and variance of Cauchy is undefined. In most cases (including your case), people can just numerically calculate standard deviation of a ratio distribution (the change order rate in your case).

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  • $\begingroup$ Ok, this makes sense. How then would I numerically calculate the standard deviation of the change order rate? $\endgroup$
    – Jake
    Dec 15, 2015 at 19:38
  • $\begingroup$ I'm not sure what you are asking, but I think the standard deviation of the change order rate is STDEV(C2:C5), which is answered in the first paragraph. $\endgroup$
    – yuqian
    Dec 16, 2015 at 2:41

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