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What is the maximum value of coefficient of variation? |
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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. |
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