## 3 Results
### Descriptive Statistics and Frequency Distribution of Activity Concentrations  
The descriptive statistics were used to infer the types of frequency distributions of the radioactivity [6,18,43,44]. The statistical parameters included the mean, standard deviation (SD), minimum, maximum, median, coefficients of variation (CV), skewness, kurtosis, and \(p\)-values from a normality test. The computing methods for skewness (\(G_{1}\)) and kurtosis (\(G_{2}\)) followed Equations (5) and (6) [45]:  
\[G_{1}=\frac{\sqrt{\{n(n-1)\}}}{n-2}g_{1} \tag{5}\]  
\[G_{2}=\frac{n-1}{(n-2)(n-3)}\{(n+1)g_{2}+6\} \tag{6}\]  
where \(g_{1}\) and \(g_{2}\) are traditional measures of skewness and kurtosis, respectively, and \(n\) is the sample size. Table 4 lists the descriptive statistics of the activity concentrations for \({}^{40}\)K, \({}^{226}\)Ra, and \({}^{232}\)Th. The mean and SD ranges are discussed in Section 3.1. To determine the spread of a probability distribution, the CV percentage was obtained by dividing the standard deviation by the mean value [6,46]. A smaller coefficient of variation implies less deviation in the data, translating into a lower risk with respect to the data. In this study, the CV percentages of the samples ranged from 29.5% to 33.7%, indicating moderate deviation in the activity concentrations [6]. This moderate deviation in radioactivity was due to certain samples, such as S14, S15, and S29, having significantly lower activity levels compared to the mean values. To assess the degree of peakedness in activity concentrations compared to a normal distribution, the kurtosis parameter can be utilized [4,25,47]. In this study, the kurtosis \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & \({}^{40}\)**K** & \({}^{223}\)**Th** & \({}^{226}\)**Ra** \\ \hline Mean, Bq/kg & 344.4 & 26.5 & 18.6 \\ SD *, Bq/kg & 116.1 & 8.4 & 5.5 \\ CV (\%) & 33.7 & 31.8 & 29.5 \\ Minimum, Bq/kg & 77.2 & 5.3 & 3.9 \\ Maximum, Bq/kg & 517.7 & 39.1 & 31.6 \\ Median, Bq/kg & 356.2 & 26.9 & 19.5 \\ Kurtosis & 0.29 & 0.98 & 2.79 \\ Skewness & \(-\)0.80 & \(-\)1.04 & \(-\)1.04 \\ \(p\)-value ** & 0.54 & 0.75 & 0.13 \\ Distribution & Normal & Normal & Normal \\ World average, Bq/kg & 420 & 45 & 32 \\ \hline \hline \end{tabular}
* Standard deviation; ** normality test through the Kolmogorov–Smirnov method.  
\end{table} 
Table 4: Descriptive statistics of activity concentrations for \({}^{40}\)K, \({}^{226}\)Ra, and \({}^{232}\)Th. values of three types of radioactivity were analyzed, and they were all positive, indicating a higher peak than the normal curve. The kurtosis values for \({}^{40}\)K and \({}^{232}\)Th were close to 0, while the kurtosis value for \({}^{226}\)Ra was 2.79 due to a concentration of activity levels within a relatively small range. Specifically, 80% (24/30) of the \({}^{226}\)Ra activity concentrations was found to fall between 15.0 Bq/kg and 25.0 Bq/kg. The skewness parameter determines whether the activity concentration is symmetrically spread around the mean value, with positive and negative values indicating right and left tails of activity concentrations, respectively [4; 25; 47]. In the present study, the skewness values for the activity concentrations of three nuclides were negative (\(-\)0.80 to \(-\)1.04), indicating that the radioactivity was slightly skewed to the left of the mean. Figure 3a-c shows the frequency distribution and the cumulative percentage curves of \({}^{40}\)K, \({}^{232}\)Th, and \({}^{226}\)Ra activity concentrations. To test the normality of the activity concentration, the K-S method was employed. The results indicate that the activity concentrations were distributed normally, with significant values of normality test exceeding 0.05, as shown in Table 4. The activity concentration for the three radionuclides was mainly concentrated in the middle data.