Marks-versus-Percentile Data: A New Method of Analysis to Determine the Preparation Level of Students

The aim of this study is to formulate a new method for an analysis of examination-related data (marks vs. percentile) to determine the average preparation level of the examinees. For this purpose, we have used a small set of marks vs. percentile data (obtained from the internet) of the Joint Entrance Examination – Main [JEE (Main)] conducted in April 2024. An empirical expression has been chosen here to represent the percentile score as a function of marks. Based on this function, we have derived an expression for the probability of scoring any marks and shown its behaviour graphically.