Estimation of percentile score based on marks obtained in an examination: A simple mathematical model

Abstract

In order to find whether a student is eligible for admission to higher academic institutions, it is often necessary to estimate the percentile score of the student, based on the marks obtained in a competitive examination. In the present article, we have discussed the formulation of a very simple mathematical model to calculate the percentile score based on the percentage of marks. For this purpose, we have defined a function representing the probability that a certain fraction of the syllabus has been studied by a candidate before appearing for the examination. Another function has been derived, in terms of that fraction, representing the probable percentage of marks obtained by the candidate. Using these functions, we have derived expressions for the expected percentile score and the rank of the candidate in terms of the percentage of marks. To determine the values of the constant parameters associated with the present model, one is supposed to use the marks-versus-percentile-versus-rank data obtained from the examination results of previous years. Due to the unavailability of these data, we have used different combinations of values of the parameters to show graphically how the percentile score and rank of a candidate vary as functions of the percentage of marks obtained in the examination.