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I think that the sentence "This result is important because it further justifies using a mean as a representative of a random set, particularly in Bayesian estimation." is a fallacious argument. As a thought experiment, I can define the set of functions D(p,q) that are minimized by the median. The existence of this set does not add any justification to using the median as a representative of a random set over any other statistic. 18.104.22.168 (talk) 17:37, 18 March 2014 (UTC)