I have a set of numbers between 0 and 1, for instance, {0.4, 0.1, 0.0, 0.8}. What are the minimum and maximum values of population variance on such set?
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1Consider the cases all 0; all 1; and half 0 and half 1. – Nick Cox Dec 04 '18 at 17:07
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Thanks @NickCox. But it also depends on the number of elements in the set. No? If I have 100 1's and 100 0's or if I have 1000 1's and 1000 0's. – Behrooz Omidvar Tehrani Dec 04 '18 at 17:11
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1Not at all. Variance or equivalently SD adjusts for sample or population size. Did you try the calculation? – Nick Cox Dec 04 '18 at 17:15
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Thanks for your response @NickCox. I did and I never obtain a value larger than 1 as population variance (dividing by N not N-1) and I wonder if it is always the case and I never get a value larger than 1. – Behrooz Omidvar Tehrani Dec 04 '18 at 17:16
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1Give an example with variance 1. – Nick Cox Dec 04 '18 at 17:34