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From: Henry on 8 Feb 2010 05:18
On 8 Feb, 08:10, Bacle <ba...(a)yahoo.com> wrote:
> Sorry for my dumbness. I realized the second condition
>  I gave is tautological, in that it is a condition that every distribution satisfies. Is symmetry necessary.?
>
> Thanks.

No, symmetry is not necessary.

Just consider the distribution which gives 1, 4, 5, 7 and 8 equal
probability. Then the median and mean are both 5.
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