What method of central tendency to use if we have irregularly high frequencies for lower values?

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Say we have a distribution with very high frequencies on the lower end but not many on the upper end. Should Median and IQR be used over Mean and Standard Deviation as we do when we have extremely large values?

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Yes, and for the same reason. An "outlier" doesn't have to be a very large value. Just a draw from the low-probability region can significantly alter the statistic. And the mean and SD are susceptible to that. Median and IQR are more robust.