Objective: The purpose of this study is to apply methods of mathematical statistics to assess and analyze the physical fitness indicators of cadets, as well as to identify statistically significant relationships between key anthropometric characteristics and physical performance indicators.

Theoretical Framework: The research is based on the theoretical foundations of mathematical statistics, including rank correlation analysis, hypothesis testing, and statistical significance assessment. The study relies on classical and modern statistical approaches used in the analysis of physical fitness and human performance indicators in educational and military training contexts.

Method: The main research methods include descriptive statistical analysis, rank correlation analysis using Kendall’s tau coefficient, and hypothesis testing at a given significance level. Empirical data on cadets’ body weight, height, and the number of pull-ups were processed by assigning ranks to the observed variables and evaluating the strength and significance of the relationships between them.

Results and Discussion: The results of the statistical analysis demonstrate the presence or absence of statistically significant rank correlations between physical fitness indicators and anthropometric characteristics of cadets. The findings allow for an objective assessment of the relationship between body weight and physical performance, highlighting the importance of applying nonparametric statistical methods in the analysis of physical fitness data.

Research Implications: The proposed approach can be used to improve the objectivity of physical fitness assessment systems in military and educational institutions. The application of mathematical statistics makes it possible to justify differentiated evaluation criteria based on individual physical characteristics.

Originality/Value:
The study contributes to the practical application of mathematical statistics in the assessment of physical fitness by demonstrating the effectiveness of rank correlation methods in analyzing real empirical data. The results can be used both in educational practice and in further scientific research related to physical training assessment.

Keywords: mathematical statistics, physical fitness, rank correlation, Kendall’s tau, hypothesis testing, cadets.