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This paper proposes a set of non-parametric statistical functions designed to analyse non-linear systems within the context of refined educational management. Recognizing the limitations of traditional parametric methods—particularly their reliance on stringent distributional assumptions this research develops a comprehensive framework that accommodates the complexities inherent in educational data, which often exhibit non-normal distributions and diverse variable types. The proposed functions enable robust evaluation of relationships among educational metrics, facilitating improved hypothesis testing and the identification of meaningful patterns in student performance and teaching effectiveness. Furthermore, the study discusses the practical application of these methods in educational settings, demonstrating their utility in evaluating program efficacy and informing data-driven decision-making processes. Through methodological innovation, this work aims to enhance analytical rigor in educational research, ultimately contributing to improved management strategies and optimized learning outcomes in dynamic educational environments. Future work will explore integration with federated learning for multi-institutional data collaboration.