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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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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.

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    $\begingroup$ 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_b Sep 24 '15 at 2:39
  • $\begingroup$ This is not true in general. See amstat.org/publications/jse/v13n2/vonhippel.html $\endgroup$ – rightskewed Sep 24 '15 at 3:07

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