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    $\begingroup$ Your point about descriptive versus inferential statistics is worthwhile. But you are effectively saying (for descriptive statistics) "only use the mean when it is the same as the median." If the distribution is skewed, then the median does a poor job of representing the concept of per capita, right? So isn't it just as valid to take the position "only use the median when it equals the mean?" That's just as arbitrary, and seems to direct attention away from the substantive meaning of these measures (for folks learning them). $\endgroup$ Commented May 5, 2014 at 5:23
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    $\begingroup$ @Alexis Though the sample mean and sample median are both estimating the same aspect of a symmetric population, they will rarely be equal for a dataset that is approximately symmetric. But yes, for all practical purposes they should be similar in which case it really doesn't matter which one to report. In choosing a numerical summary measure of the distribution to replace a graphical display, the goal is not represent the concept of per capita. In other contexts, I agree with you and the others that the appropriate measure of center should depend on the research question. $\endgroup$ Commented May 5, 2014 at 7:00
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    $\begingroup$ @Alexis Perhaps we are thinking about things differently, but I don't think that's any reason to respond rudely. Why don't you try giving an example to illustrate your point instead of acting argumentative and shocked that I could espouse such a view. $\endgroup$ Commented May 5, 2014 at 16:29
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    $\begingroup$ I don't see any rudeness or "acting shocked" coming from the OP...just sayin'... $\endgroup$ Commented May 5, 2014 at 17:53
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    $\begingroup$ @PeterFlom What about in cases where the end goal is not inference? I agree that the appropriateness of a descriptive statistic depends entirely on the reason for producing the statistic. The notion that it is possible that "no descriptive measure makes sense" seems to imply that a descriptive statistic cannot be inherently meaningful. I would argue that in almost all cases, the median makes sense as a measure of the center of the distribution by definition. Whether or not it makes sense for other purposes is another question. $\endgroup$ Commented May 5, 2014 at 20:14