What would cause the mean to be less than the median, and under what conditions would the mean and the median be close to one another?
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4$\begingroup$ Any distribution with mean > median can be reflected about the mean (or median) to get a distribution with median > mean. $\endgroup$– Nuclear HoagieCommented Aug 12 at 14:20
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1$\begingroup$ [-100000, 2, 3] $\endgroup$– John MaddenCommented Aug 12 at 14:21
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$\begingroup$ stats.stackexchange.com/questions/3787/…, stats.stackexchange.com/questions/251701/…, stats.stackexchange.com/questions/569181/…, stats.stackexchange.com/questions/89382/…, stats.stackexchange.com/questions/89382/… $\endgroup$– kjetil b halvorsen ♦Commented Aug 12 at 14:46
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1 Answer
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The mean would be less than the median if the distribution is negatively skewed. In other words, the mean is less than the median when the distribution of scores is not symmetrical and there are more extreme scores in the bottom 50% than in the top 50%.
The mean and median will align when the distribution of scores is perfectly symmetrical, and they will be "close to one another" when the distribution is nearly symmetrical.
answered Sep 24, 2015 at 0:58
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4$\begingroup$ How are you defining "negatively-skewed"? Note also that the distribution needn't be symmetrical for mean and median to coincide. While what you say is often the case it's not always the case. $\endgroup$– Glen_bCommented Sep 24, 2015 at 2:39
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2$\begingroup$ This is not true in general. See amstat.org/publications/jse/v13n2/vonhippel.html $\endgroup$ Commented Sep 24, 2015 at 3:07