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Statistical modeling reveals student score distributions from marks-versus-percentile examination data, suggesting a simple method to quantify overall candidate preparation.
This study presents a simple method for analysing marks-versus-percentile data from an examination. The main purpose is to obtain a measure of the overall preparation level of the examinees. The method is developed using marks-versus-percentile data for the Joint Entrance Examination–Main [JEE (Main)] held in April 2024. An empirical mathematical function is used to describe the relation between marks and percentile score. From this function, a probability function for obtaining different marks is obtained. This probability function is then used to find the most probable marks, the average marks, and the standard deviation of marks. The probability of obtaining marks within a specified range and the probability of obtaining marks equal to or greater than a specified value can also be calculated. For the data used in this study, the fitted function gives a coefficient of determination of 0.99894. The most probable marks are found to be 19, while the expectation value and standard deviation are 47.26 and 49.74 marks, respectively. The sum of the calculated probabilities is very close to unity. The method is simple and can be applied to other examinations. Its accuracy can be improved by using a larger marks-versus-percentile dataset.
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Sudipto Roy (2026) studied this question.
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