This study presents a simple mathematical method for analysing examination-related data and describing the overall performance of a group. A hypothetical dataset of scores and percentile values is used to demonstrate the method. An empirical formula is fitted to the percentile data. From this formula, a probability distribution is obtained. This distribution is then used to find the most probable score, the average score, the spread of scores, and the probability of obtaining a score within a given range or above a given level. The method also shows how percentile values can be estimated from scores when suitable model parameters are available. It provides a simple way to study the distribution of scores and to obtain useful measures of the performance of a group. The method can also be applied to data from an actual examination. However, the results presented in this study are only illustrative because the dataset is hypothetical and is based on a limited set of data. The results should therefore not be taken as an exact description of any particular examination. More reliable results would require a sufficiently large and representative dataset from previous examinations. The accuracy of the estimates will depend on the amount and quality of the data used to determine the model parameters.
Percentile Score, Most Probable Marks, Marks-versus-Percentile Record, Probability Distribution, Statistical Analysis, Mathematical Modelling.
Sudipto Roy. Marks-versus-Percentile Data: A Simple Mathematical Analysis Based on a Hypothetical Dataset. Indian Journal of Modern Research and Reviews. 2026; 4(8):107-113
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