What is the Coefficient of Variation for this Calculation?

[Darsh]

Homework Statement

I'm stuck trying to find the coefficient of variation of this calculation: 18.97(+/-0.04) + 0.0025(+/-0.0001) + 2.29(+/- 0.08)= 21.2625. The numbers in parenthesis are the standard deviations for each value.

Homework Equations

The Attempt at a Solution

I found the overall standard deviation for the equation but now I don't know what to do to go farther. I worked some example problems with the answers in the back of the book and I got close to the correct answer on all three of them by dividing the overall standard deviation by the sum of the problem. However, I don't think this is correct and my book has no examples of finding the CV of a problem like this. Any help would be appreciated!

 

[HallsofIvy]

Think of it this way: if every individual "measurement" were at its largest exteme, we would have 18.97+0.04 + 0.0025+ 0.0001 + 2.29+ 0.08= 21.2625+ (0.04+ 0.0001+ 0.08)= 21.2625+ 0.1201. If each were at it smallest extreme we would have 18.97- 0.04+ 0.0025- 0.001+ 2.29- 0.08= 221.2625- 0.1201.

$18.97\pm 0.04+ 0.0025\pm 0.0001+ 2.29\pm 0.08= 21.2525\pm 0.1201$.

 

[Architeuthis Dux]

The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation by the mean of the data set. In this case, the mean of the data set is 21.2625. Therefore, the CV can be calculated as follows:

CV = (Standard deviation / Mean) * 100% = [(0.04 + 0.0001 + 0.08) / 21.2625] * 100% = 0.000416 * 100% = 0.0416%

This means that the overall variability of the data set is relatively low, as the CV is less than 1%. This information can be useful in comparing the variability of this data set to others, and in assessing the precision and accuracy of the measurements used in the calculation. It is important to note that the CV is only useful when comparing data sets with similar units and scales.