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Thread: Finding the Min and Max of a range when I know the 25th, 50th, and 75th Percentiles

  1. #1

    Finding the Min and Max of a range when I know the 25th, 50th, and 75th Percentiles

    Hi All,

    I'm trying to figure out if there is a way to calculate the minimum and maximum of a range where I already know the values of the 10th, 25th, 50th, 75th, and 90th percentiles.

    Min 10th 25th 50th 75th 90th Max
    ? 119 137 155 173 191 ?

    I've done a bunch of searches on Google and various sites and I'm not sure if I'm just phrasing my question poorly but I can't find anything.

    Thanks in advance.

  2. #2
    Full Member
    Join Date
    Mar 2016
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    Unfortunately, what you're seeking is not possible. Consider the data set {118, 119, 119, 137, 137, 137, 140, 140, 140, 155, 155, 160, 160, 173, 173, 173, 191, 191, 200}. This meets all of your percentile requirements. The minimum is 118 and the maximum is 200. But now replace the 118 with 0. The five percentiles didn't change, but the minimum is now 1. Similarly, you can replace 200 with a trillion and not change the percentiles. Hence, the only thing you can possibly say about the minimum and the maximum is that the minimum value is at most 119 and the maximum is at least 191.

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