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If it is of any one's interest, the data is taken from the duration of men "last in bed" as studied here.

I want to calculate the percentiles (say, 95th) of a non-normal distribution without raw data. What are the minimum constraints needed? I have the following and I think some are not necessary.

  • n=474
  • mean=8.5
  • SD=7.47
  • median=6.0
  • min=0.1
  • max=52.7
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  • $\begingroup$ There's an infinite number of possible solutions. It might be possible to derive some bounds $\endgroup$
    – Glen_b
    Commented Apr 1, 2019 at 14:46

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This is not possible. The percentile depends on the exact shape of the distribution. So unless you make a parametric assumption about the distribution or an assumption directly about the 95th percentile you cannot estimate the percentile well without the original data.

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