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> but I thought the mean is considered an improper metric for the "average" value of asymmetric distributions.

It entirely depends on what you are looking to explain or describe.

Mean is appropriate for investment returns if you can diversify risk over many investments. Median is appropriate for looking at incomes in terms of social policy. 95th or 99th percentile might be appropriate when you are looking to ensure that your web server provides reliable response times.




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