Centroid Based Clustering Models for Designing Dense Ranking of Schools Focusing on Total Marks of Individual Students in a Common Examination

This research aims to tackle the inherent challenges in establishing equitable and comprehensive methodologies for ranking schools, particularly concerning assessments based on students' test performances. Conventional ranking systems often fail to account for the diverse student demographics within schools, resulting in inadequate representations of their achievements and frequent ties in rankings. In response, the proposed ranking methodology introduces a clustering process that categorises students into distinct groups based on their academic marks. An adequate school ranking is established by examining the distribution of student volumes and marks within these groups. It ensures a holistic portrayal of each school's performance by considering both the quality of grades and the number of students involved. The study uses k-Median clustering algorithm as the basis for school rankings. The primary objective of this paper is to compare the effectiveness of k-Median and k-Means algorithms. In addition, various graphical techniques such as histograms, elbow plots, silhouette analysis, gap statistics, and Davies-Bouldin Index (DBI) are employed to determine the optimal number of clusters <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(k)$</tex> used in k-Median and k-Mean clustering. Further, diverse cluster analyses are conducted, and school statistics are explored to ensure an accurate assessment of school performance. The efficacy of this novel approach is validated through a case study, illustrating its ability to establish fair, meaningful, and reliable rankings for the schools under consideration.