## 3 Experimental Design
### Variable Analysis  
#### 3.2.1 Univariate Analysis  
Univariate analysis [32] serves as a foundational step in this study, offering critical insights into the distribution, variability, and potential anomalies of individual features. Through the use of histograms, kernel density estimation (KDE) plots, and boxplots, it becomes possible to identify key data characteristics such as multimodal distributions, outliers, and skewness--factors that are essential for guiding subsequent data cleaning, normalization, and transformation processes.  
Figure 2 visualizes the distribution of various physical fitness indicators among university students using histograms with kernel density estimation (KDE) curves and boxplots. The histograms show the frequency of values for each variable, with the KDE curve revealing the overall distribution and potential modes. This helps identify characteristics like multimodal distributions, skewness, and outliers, which guide data preprocessing. For example, the weight score shows a bimodal distribution, indicating the presence of both underweight and overweight/obese groups, while the sit-up score is right-skewed, suggesting that many students struggle with this test. The boxplot adds further detail, showing  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Weight**} & \multirow{2}{*}{**BMI**} & **Lung Capacity** & **50 m** & **Standing** & **Sitting** & **1000 m** & **Pulling Up** & \multirow{2}{*}{**Total Score**} & \multirow{2}{*}{**Year**} \\  & & **Capacity** & **Running** & **Long Jump** & **Forward** & **Running** & **Score** & & \\  & & **Score** & **Score** & **Bend Score** & **Score** & **Bend Score** & **Score** & **Bend Score** & **Score** \\ \hline
100 & 23.80 & 80 & 90 & 90 & 90 & 78 & 68 & 85.4 & 2020 \\
60 & 21.08 & 90 & 100 & 100 & 76 & 90 & 100 & 94.1 & 2020 \\
100 & 19.72 & 78 & 74 & 78 & 90 & 72 & 64 & 79.1 & 2021 \\
80 & 23.63 & 100 & 74 & 78 & 100 & 66 & 10 & 76.8 & 2021 \\
100 & 19.  
the interquartile range (IQR), with outliers represented by dots outside the whiskers. For instance, the weight variable shows significant variability with many outliers, and the Lung Capacity Function Score has a slight right skew, with some low outlier scores. The sit-and-reach and standing long jump scores show near-normal distributions, while the 800 m run has a multimodal distribution, likely due to differences in endurance across subgroups. Lastly, the year variable is evenly distributed across academic years (2020-2023), as shown by both the histogram and boxplot. This temporal consistency ensures that the dataset is not biased by any specific year, enhancing the generalizability of the findings across all years. Analyzing the year variable helps confirm the validity of the data and strengthens the study's conclusions.  
Figure 2: Univariate analysis results for each column of the dataset.  
The integration of univariate analysis is motivated by its ability to enhance the accuracy, robustness, and interpretability of clustering and machine learning models. By enabling a detailed understanding of the behavior of each physical fitness indicator, this approach ensures that meaningful patterns are preserved and not masked by noise or inconsistencies in the dataset. Furthermore, isolating the distributional properties of individual variables facilitates the development of precise, evidence-based intervention strategies tailored to the specific health profiles of college students, thereby increasing the practical relevance and scientific impact of the study's findings.