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I checked multiple sources on the internet about which is the better, mean or median. They say that IF there are outliers in the data or if the data is skewed then the median is better. They also say that the median is close to the mean if the data is not skewed(for example: Normal distribution).

But Doesn't that imply that the median is always better or at least as good as the mean for summarizing the data?
In skewed distributions and distributions with outliers -> the median is better than mean
In symmetric distributions(for example: Normal distribution) -> the median is the same as the mean

floyd
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    Can you clarify what you mean by "better"? I see you mean something along the lines of "for summarizing the data", but I am not sure what this means precisely. – Galen Aug 28 '22 at 05:01
  • I learned that "descriptive statistics" is used to summarize information about datasets. mean and median are numbers that summarize datasets. I wanted to know what the best way to summarize a dataset or a distribution is. – floyd Aug 28 '22 at 05:05
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    I think you'll find that there is no ultimately-best way to summarize data. The mean and median tell us different things. – Galen Aug 28 '22 at 05:12
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    The mean can be more appropriate than the median even if outliers are present. For example, your annual expenditure may be very different in any year in which you buy a house or a car, but the mean expenditure is linked to the sum of expenditures over several years and is the summary of concern. You and your bank manager and anybody in your family have no practical interest in the median annual expenditure. – Nick Cox Aug 28 '22 at 06:38
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    Just about any decent introductory statistics textbook will give a more nuanced account than you are gleaning from internet surfing. One excellent example, is Freedman, Pisani, Purves, Statistics, any edition. – Nick Cox Aug 28 '22 at 06:39

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