Question

What is the maximum value of coefficient of variation?​

Answer 1

Answer:

What is the maximum value of σxx¯, the coefficient of variation, over all choices of the xi's in the interval [0,c]?

The maximum value that I can find for σxx¯ is n−1−−−−−√ which is achieved when n−1 of the xi have value 0 and the remaining (outlier) xi has value c, giving

x¯=cn, 1n∑x2i=c2n⇒σx=c2n−c2n2−−−−−−−√=cnn−1−−−−−√.

But this does not depend on c at all, and I am wondering if larger values, possibly dependent on both n and c, can be achieved.

Answer 2

Answer:

Coefficient of variation =( standard deviation / mean deviation ) * 100

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