Discussion
If \(\overline{X}\) = 100, \(\sigma_{x}\) = 10, \(\overline{Y}\) = 200, \(\sigma_{y}\) = 15, then :
Answer: B
The answer is C.V. (X) > C.V. (Y).
The coefficient of variation is the standard deviation as a percentage of the mean:
\[ \begin{aligned} CV_{X} &= \frac{10}{100} \times 100 = 10\% \\ CV_{Y} &= \frac{15}{200} \times 100 = 7.5\% \end{aligned} \]
Although Y has the larger standard deviation, X varies more relative to its mean, so X is the less consistent series. The ratio of the two is 10/7.5, about 1.33, not 1.5, so the last option is also wrong.
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