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In statistics, the percentile rank of a given score is the percentage of scores in its frequency distribution that are less than that score. Its mathematical formula is
where CF—the cumulative frequency—is the count of all scores less than or equal to the score of interest, F is the frequency for the score of interest, and N is the number of scores in the distribution. Alternatively, if CF' is the count of all scores less than the score of interest, then
The figure illustrates the percentile rank computation and shows how the 0.5 × F term in the formula ensures that the percentile rank reflects a percentage of scores less than the specified score. For example, for the 10 scores shown in the figure, 60% of them are below a score of 4 and 95% are below 7. Occasionally the percentile rank of a score is mistakenly defined as the percentage of scores lower than or equal to it, but that would require a different computation, one with the 0.5 × F term deleted. Typically percentile ranks are only computed for scores in the distribution but, as the figure illustrates, percentile ranks can also be computed for scores whose frequency is zero. For example, 90% of the scores are less than 6.
In educational measurement, a range of percentile ranks, often appearing on a score report, shows the range within which the test taker's "true" percentile rank probably occurs. The "true" value refers to the rank the test taker would obtain if there were no random errors involved in the testing process.