Percentile

A percentile is a statistic that gives the relative standing of a numerical data point when compared to all other data points in a distribution. In the example PM − 66, P.84 is called the percentile rank and the data point of 66 is called the percentile point. The .84 in the percentile rank of P.&j is a proportion that tells us the relative standing of the percentile point of 66 compared to all other data points in the distribution being examined. Reporting percentiles can be a useful way to present data in that it allows an audience to quickly determine the relative standing of a particular data point.

By itself, a raw score or data point says little about its relative position within a data set. Percentiles provide a number expressing a data point's relative position within a data set. At a glance, the percentile shows the reader whether a particular numerical data point is high, medium, or low in relation to the rest of the data set. Salaries, IQ scores, standardized test scores such as the SAT, GRE, body mass index (BMI), height, and weight are all frequently expressed as percentiles.

Some percentile values commonly used in reporting are the median, P.50, below which 50% of the cases fall; the lower quartile, P 25, below which 25% of the cases fall; and the upper quartile, P75, below which 75% of the cases fall. The area between the lower quartile and the middle quartile is called the “interquartile [Page 579]range,” which contains the middle 50% of values in a distribution.

There are two basic definitions of the proportion expressed in the percentile rank. One definition used in some introductory statistics textbooks calculates the percentile rank as the proportion of cases falling below the percentile point. Using this definition, the maximum obtainable percentile must be less than 1.0, because there is no number in a data set that falls below itself. The second definition of percentile rank is the proportion of cases at or below the percentile point. Using this second definition, the 100th percentile is the maximum obtainable percentile, because 100% of the data falls at or below the largest number in a data set. The definition of percentile is dependent on the formula used to calculate the percentile rank.

Using our example P.84 = 66, the first definition of percentile rank calculates the percentile rank of .84 to mean 84% of the cases in the distribution fall below the percentile point of 66. A relatively simple way to calculate percentiles using this definition can be obtained with the formula p(N) where p is the desired percentile rank and N is the number of cases in the distribution. This calculation gives the position within the distribution where the percentile point is located once the data points in the distribution are ordered from lowest to highest. If p(N) results in a fractional number, round up to the next highest number for the percentile point position within the distribution. Once the position within the data set is determined, count up from the bottom of the distribution to the number obtained from the calculation p(N). The mean of that number in the data set and the number value in the next highest position in the distribution is the percentile point corresponding to the percentile rank.

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