Conditions to Have Mean=Median
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From: Bacle on 7 Feb 2010 16:56 Hi, everyone: I am trying to see what the necessary/sufficient conditions on a distribution , to have the mean equal the median. It seems like symmetry is at least sufficient; the normal distribution obviously has this property. In general, it would seem that if there is a value m in the distribution such that , when removing m ,half the data points are left of m, and half are right of m, then the mean agrees with the median. This is weaker than ( but obviously includes the case of) symmetry. We would paste together (continuously) one curve C_L left of m that integrates to 1/2, (with limit m on the right), with a curve C_R right of m (with limit m on the left) , so that C_R integrates to 1/2. Is this last condition the weakest possible to guarantee that the mean equals the median.? Thanks. |