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If the skewness is different, then the data sets are different.

Incidentally, there is one [largely obsolete] definition of skewness which is in terms of the mean and median. Under that definition, it would be impossible for two data sets to have equal means and equal medians but opposite skewness.

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Q: Would you consider two data sets similar or different if they have the same mean median and range but one is positively skewed and other negatively skewed?
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