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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