tag:blogger.com,1999:blog-715339341803133734.post4453045449539329914..comments2017-09-02T00:54:30.857-05:00Comments on Maximum Entropy: Mean vs median - a careful balancing actTom Campbell-Rickettshttp://www.blogger.com/profile/07387943617652130729noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-715339341803133734.post-8399866827265472762015-04-28T18:15:51.418-05:002015-04-28T18:15:51.418-05:00Quite right, thanks for pointing it out.
Thinkin...Quite right, thanks for pointing it out. <br /><br />Thinking about it drew a couple of other points to mind, which I've also reflected in a minor edit or two:<br /><br />(1) I tacitly assumed the uniqueness of the median, throughout, in effect assuming a continuous distribution.<br /><br />(2) The relationship between the mean and median is not uniquely determined by the direction of skew. Hence, I added the word 'typically' in the sentence: <br /><br />"If a distribution has an extended tail on one side only, then the mean will typically be positioned further out into the tail than the median. " <br /><br />Cheers.Tom Campbell-Rickettshttps://www.blogger.com/profile/07387943617652130729noreply@blogger.comtag:blogger.com,1999:blog-715339341803133734.post-13987237485448774182015-04-28T16:40:49.207-05:002015-04-28T16:40:49.207-05:00"(all such distributions are symmetric, and v...<i>"(all such distributions are symmetric, and vice versa)."</i><br /><br />Really? All symmetric distributions have the same mean and median, but the reverse is in general not true. Say income is distributed as a Gaussian and each person earns an integral number of pounds. Let the top earner earn a pound more. This moves the mean to the right but not the median. Move the mean back to its original position by giving 100 people to the left of the mean one penny more. The resulting distribution has the same mean and median, but is not symmetric.<br />Phillip Helbighttps://www.blogger.com/profile/12067585245603436809noreply@blogger.comtag:blogger.com,1999:blog-715339341803133734.post-889822714618889192015-04-28T16:38:26.022-05:002015-04-28T16:38:26.022-05:00This comment has been removed by the author.Phillip Helbighttps://www.blogger.com/profile/12067585245603436809noreply@blogger.com