Percentile Rank Computation

 In statistics, the percentile rank (PR) of a given score is the percentage of scores in its frequency distribution that are less than that score. Percentile provides a relative rank in a distribution which is based on a scale of 100. The percentile rank of a score tells what percentage of scores lies below that particular given percentile rank. 

Because the percentile rank indicates the position of a score in reference to ranks, thus it is an ordinal statistics. There is no sense of a rank, until and unless the total number of score is known in a distribution.

 Percentile rank has a universal meaning, which is not found in original scores. Any percentile rank near zero, means a low position in the group, similarly a PR near 50 means average position in the group and PR near 100 always have a high position in the group. The percentile rank tells the position of an individual in a group, it is not an absolute value. Also it is essential to know the nature of the group in evaluating a percentile rank of an individual.

Calculating Percentile Rank

Percentile ranks can be computed from organized data, as well as from serially arrange score. When scores are arrange in a serial order, then percentile rank PR can be computed from the following formula:

P R=100- 100R-50N

Where, 

       P R = Percentile Rank

          R = Rank of score

          N = Total number of scores.

From Grouped data

When data is grouped then PR is calculated from the following formula:

P R= 100NF- X-Lfqi

Where,

X = The score for which P R is to be calculated

L = Exact lower limit of the class interval in which X lies.

fq = Frequencies of the class interval in which X lies.

F = Cumulative frequencies below the class-interval in which X lies.

N = Total number of frequencies.

 i  =  Size of the class-interval.

Steps for calculating P R

1. Find out the class interval in which the score falls, for which P R is ought.

2. Find out the exact lower limit of the class interval in which X lies.

3. Calculate the cumulative frequencies (F).

4. Divide the frequencies of desired class- interval by the size of class interval (i) to find out the rate of step deviation.

5. Multiply the difference of  X and exact lower limit by the rate of step deviation.

6. Add this product to the cumulative frequencies below the class interval, in which X lies.

7. Multiply this sum by 100.

8. The result of step seven now be divided by N. One can reverse the process of step 7 and 8, i.e. first divide the sum by N and then multiply it by 100.