## 5 Data Statistical Analysis  
The current data was statistically analyzed using both the Origin Pro 2019b and IBM SPSS statistics (version 23) software packages. The numerical and graphical outputs extracted from the statistical analysis were used for investigating the normality distribution of radioisotope concentrations and radiological parameters. Descriptive statistics for simplifying data by reducing it into a simple summary were performed. The descriptive statistics calculated include the minimum (Min), maximum (Max), mean, range, variance, standard deviation, kurtosis, and skewness (Table 5). The histogram together with the frequency distribution curve were determined and compared with the function of normal distribution using the Shapiro-Wilk and Anderson-Darling tests (\(p\)-value \(>\) 0.05). Additionally, the potential linear relationships among variables were also statistically introduced herein via Pearson correlations analysis. For all variables (Table 5), standard deviations that are less than the means indicate a high degree of uniformity. However, the positive small values of the skewness of the radioisotopes (\({}^{348}\)U, \({}^{232}\)Th, and \({}^{40}\)K) concentrations, as well as those for other parameters (Table 5), indicate that their distributions are not perfectly symmetric and deviated to the right (positive skewed). Moreover, kurtosis is a small negative of most of the variables  
Figure 13: Variation in \(\text{IYED}_{\text{Rn}}\) in the investigated samples. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multirow{2}{*}{**Range**} & \multirow{2}{*}{**Min**} & \multirow{2}{*}{**Max**} & \multicolumn{3}{c}{**Mean**} & \multicolumn{3}{c}{**Std. **} & \multirow{2}{*}{**Variance**} & \multirow{2}{*}{**Skewness**} & \multirow{2}{*}{**Kurtosis**} & \multirow{2}{*}{**Normality Test**} & \multirow{2}{*}{**GFT for Normal**} \\  & & & & & & & & & & & (Shapiro-Wilk) & **Distribution** \\ \cline{5-10}  & & & & & & & & & & & & & & \\ \cline{5-10}  & & & & & & & & & & & & & & \\ \hline \({}^{238}\)U & 55.110 & 16.890 & 72.000 & 38.726 & 3.379 & 15.111  
reported herein as shown in Table 5. Therefore, a small flatter peak and small thinner tails distribution are assumed. The normality of distribution for all variables was tested using the Shapiro-Wilk test. The \(p\)-values of the Shapiro-Wilk test for radioisotopes (U-348, Th-232, and K-40) concentrations and for radiological risk parameters are all greater than 0.05 (Table 5), confirming that the current data follows a normal distribution. To validate this, the Anderson-Darling test (A-D test) was used in conjunction with the goodness of fit test (GFT) for normal distribution. The findings show that the data set for the radioisotopes (U-348, Th-232, and K-40) concentrations and other radiological variables also follow the normal distribution where \(p\)-values greater than 0.05 for the normal test (Table 5). The frequency distributions of radioisotopes concentrationsas well as those of radiological variables (Figures S1-S9 in the Supplementary Material) were shown (Figures 14-16). The majority of the histograms show some degree of bimodality. The bimodal distributions of radioisotopes in ElSibai-Abu EITjur granites reflect the different processes that the magma undergo during its ascending to the surface. Pearson correlations are provided to demonstrate the potential linear relationships between the concentrations of U-238, Th-232, and K-40 and the radiological parameters (Table 6). It is evident that all considered variables are positively correlated with each other.