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
Find out the class interval in which the score falls, for which P R is ought.
Find out the exact lower limit of the class interval in which X lies.
Calculate the cumulative frequencies (F).
Divide the frequencies of desired class- interval by the size of class interval (i) to find out the rate of step deviation.
Multiply the difference of X and exact lower limit by the rate of step deviation.
Add this product to the cumulative frequencies below the class interval, in which X lies.
Multiply this sum by 100.
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.
