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The definition presented below provides for a unique measure for each unique value of s that corresponds to the PERCENTILE.EXC macro in Excel. This version starts by computing \((n+1)s\) where \(0 < s < 1\) and using this to linearly interpolate between two adjacent entries in the sorted list. Another option that corresponds to PERCENTILE.INC (and PERCENTILE) in Excel is to start with \((n-1)p+1\) for determining how to pick the two adjacent entries and then proceeding with linear interpolation. Again, the definition below utilizes the first approach.
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