## 4 Exploratory Data Analysis
To further characterize the distribution, quantiles were calculated: the minimum value was 1.14, the 25 th percentile was 2.27, the median (50 th percentile) was 2.77, the 75 th percentile was 3.63, and the maximum value was 5.37. Based on the relationship between the mean and median, the distribution appears to be right-skewed, as the mean (2.95) is greater than the median (2.77). This indicates the presence of relatively more large values than small values in the sample, resulting in a longer tail on the right side of the distribution, with most values concentrated on the left. The statistical summary offers valuable insights into the variable's distribution, demonstrating a right-skewed pattern. These descriptive statistics, along with the quantiles, provide a comprehensive understanding that can inform further statistical analyses and decision-making processes. The ability to walk, as measured by the MWT, serves as a critical functional indicator within the patient cohort. Table 5 presents the descriptive statistics of the MWT data, which is complete and free from missing or inconsistent values, underscoring the dataset's high quality. The mean MWT distance is 399.11 m, with a SD of 106.55 m, indicating a moderate spread of walking distances around the average. The quantiles further characterize the distribution: the minimum value is 120 m, the 25 th percentile is 167 m, the median (50 th percentile) is 378 m, the 75 th percentile is 593 m, and the maximum value reaches 699 m. These quantiles offer insight into the distribution of walking ability across the cohort, \begin{table}
\begin{tabular}{c c c} \hline Validity & 100\% & \\ \hline Missing values & 0\% & \\ \hline Mean & 2.95 & \\ \hline Standard Deviation & 0.97 & \\ \hline Quantiles & 1.14 & min \\ \hline  & 2.27 & 25\% \\ \hline  & 2.77 & 50\% \\ \hline  & 3.63 & 75\% \\ \hline  & 5.37 & max \\ \hline \end{tabular}
\end{table} 
Table 4: Descriptive statistics with FVC variables. \begin{table}
\begin{tabular}{c c c} \hline Validity & 100\% & \\ \hline Missing values & 0\% & \\ \hline Mean & 399.11 & \\ \hline Standard Deviation & 106.55 & \\ \hline Quantiles & 120 & min \\ \hline  & 167 & 25\% \\ \hline  & 378 & 50\% \\ \hline  & 593 & 75\% \\ \hline  & 699 & max \\ \hline \end{tabular}
\end{table} 
Table 5: Best MWT variable descriptive statistics. showing that while most patients walk distances clustered near the median, there is variability extending towards both lower and higher extremes. Figure 5 complements these statistics with a density plot, visually illustrating the distribution of MWT distances. This plot facilitates the identification of patterns such as clustering around the median and potential skewness, enabling a more intuitive understanding of the functional capacity within the group. Figure 6 illustrates the density plot of pack history, providing a clear visual representation of the distribution of smoking exposure among the study participants. The plot highlights the frequency and concentration of pack-year values, showing that while most individuals have a moderate smoking history, a smaller subset exhibits significantly higher lifetime tobacco exposure. Following this, Table 6 summarizes the descriptive statistics of pack history, defined as the number of packs of cigarettes smoked per day over one year. The dataset is complete  
Figure 5: Density plot-best MWT. Figure 6: Density plot-pack history. with 100% validity, containing no missing or inconsistent values, which underscores its reliability. The mean pack history is 39.7, indicating the average cumulative exposure, with a SD of 24.4, reflecting considerable variability around the mean. A larger SD denotes a wider spread of pack history values, while a smaller SD would indicate values more tightly clustered near the mean. The quantiles further characterize the distribution: the minimum value is 1, the 25 th percentile is 20, the median (50 th percentile) is 36, the 75 th percentile is 54, and the maximum value reaches 109.