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There is no standard definition of a percentile, but three common definitions yield similar, if not identical, results when working with a large sample size. Some define a percentile to be the smallest value that a specified percentage of the observations is less than. Another definition is that a percentile is the smallest value that a specified percentage of the observations is less than or equal to, and this is commonly what is referred to as the percentile rank. Conveniently, a third definition that uses both of the previous two exists and handles small data sets consistently. This third method is recommended by the National Institute of Standards and Technology (NIST) for identifying percentiles and is used here.

Calculation

Notation

Y(p)the pth percentile
nthe sample size, or the number ...
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