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The variables X and U are connected by the equation X = 5 + 2U. If the mean of X is 10 and its coefficient of variation is 2.6, what is the coefficient of variation for U?
- 5.2
- 2.6
- 1.3
- 52
Correct answer: 5.2
Solution
X=5+2U: mean_X=5+2*mean_U=10 so mean_U=2.5; sd_X=2*sd_U. CV_X=sd_X/mean_X. CV_U=sd_U/mean_U=(sd_X/2)/2.5=sd_X/5. Since CV_X=sd_X/10, sd_X=10*CV_X, giving CV_U=2*CV_X=2*2.6=5.2 (idx 0). Stored 2.6 is wrong.
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