Percentile Rank

Calculation of Percentile Ranks in Simple Frequency Distributions

Calculation of percentile ranks (PR) in a simple frequency distribution is based on the assumption that [Page 773]each score is the midpoint of a range of possible scores (e.g., for X = 8, the interval from 7.5 to 8.5). Finding the percentile rank of a score thus involves finding the cumulative frequency for the midpoint of the interval (cfmp) corresponding to the score of interest and involves the following steps:

• 1.

  Find the cumulative frequency for the midpoint of the interval (cfmp) of the score of interest by averaging the cumulative frequency of the score with the cumulative frequency of the score below it. For example, for X = 8 in Table 1,

  
• 2.

  Divide the cfmp by the total frequency (F) of the distribution. Thus, for X = 8,

  
• 3.
  Multiply the resulting proportion by 100 and round to the nearest whole number to find the percentile rank (e.g., 0.33 × 100 = 33).

For ease of computation, the formula that summarizes this procedure (in which N is the total number of scores) can be simplified as follows:

In Table 1, note that the percentile ranks of scores of both 0 and 1 are shown as 1, even though no one received a score lower than 1. This is true because by convention, percentile ranks are reported on a scale from 1–99.

Calculation of Percentile Ranks in Grouped Frequency Distributions

When frequencies are reported in tables with intervals greater than one (sometimes referred to as grouped frequency distributions), percentile ranks are estimated based on the assumption that the scores are evenly distributed throughout the interval. For example, Table 2 is an excerpt from a frequency distribution of 200 scores on a 100-point scale. Although the intervals typically are depicted using whole numbers (e.g., 61–65), this is shorthand for intervals that extend beyond the values shown to their real limits (i.e., 60.5–65.5). The computational formula for percentile rank of a score (PRX)

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