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Thread: Interquartile range: Why add 1 to the sample size

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    Interquartile range: Why add 1 to the sample size




    My understanding is that the interquartile range is calculated by taking the difference between the (N+1)*0.75th observation and the (N+1)*0.25th observation. For example, with 7 observations, one would take the difference between observations 6 and 2.

    My question is this: Why do we add 1 to the sample size in this calculation? This isn't done when taking the median, so I'm wondering why it's done when taking percentiles.

    Thanks very much in advance.

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    Re: Interquartile range: Why add 1 to the sample size


    I think there is no universal formula to calculate the sample quartile.

    Even in your case, you do not guarantee n + 1 is divisible by 4;
    Round up/down already result in two different estimates.

    So just live with one of the reasonable estimates is ok.

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