## An Application Example
### Application
#### 3.2.2 Results and Discussion  
The computation is based on the drilled well's petrographic proportion data. According to drilling coring or logging, the distribution of sandstone in each well is categorized, and the average proportion of sandstone is computed using the distribution of sandstone in each well (Table 1). The sample standard deviation in this instance is 7.52, the DOF is 4, and the relative \(\tau\) value at the 95% confidence level is 2.776. The value of error \(p\%\) can be calculated using formula 4 and the calculated characteristic values. The mean sandstone proportion's optimistic and pessimistic estimates can then be determined. These values are listed in Table 4.  
As a result, three levels of sandstone proportion are established at the 95% confidence level. The optimistic estimate is 95.665%, signifying the greatest sandstone proportion; the pessimistic estimate is 76.987%, signifying the lowest sandstone proportion; the mean value is 86.326%, representing the closest sandstone proportion; and the error \(p\%\) is around 10.8%. If the proportion of the deterministic facies is determined solely by the mean value, the uncertainty may be disregarded, leading to a single computation result that cannot identify the error. The confidence interval theory-based approach of calculating the sandstone proportion yields an estimate interval. The genuine facies proportion value has a 95% likelihood of being inside the confidence interval, which is made up of optimistic and pessimistic values. The results that are estimated after accounting for error are more valuable and reliable. The intuitive data representation error \(p\%\) is useful for expressing uncertainty. The three level values provide precise values for the underground sandstone proportion's boundary range, quantifies some of the uncertainty, provides sandstone proportion values under various level conditions for reserve calculation and reservoir modeling, and provides elastic support for later exploration and development decision deployment. The dataset's degree of dispersion is indicated by the standard deviation. Therefore, the standard deviation has an effect on the value of the error \(p\%\). The ratio of the standard deviation to the mean is known as the coefficient of variation. Indirectly reflecting the size of uncertainty, the size and variation of the coefficient of variation also reflect the fluctuation of error \(p\%\). The closer the relationship between the sample mean and the population mean is in a normal distribution study, the more samples are used. However, this method is based on a t distribution and has low requirements for sample size, so it is also applicable for low samples, and there is no need to worry about the small number of samples without principle support. The underlying presumption, though, is that the raw data is as normally distributed as feasible, which can have a big impact on how satisfied people are with the outcomes. We also need to pay attention to data processing and optimization. In \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Mean (\%)** & **S (\%)** & **C** & \(\tau\) & \(p\) (\%) & **Pessimism (\%)** & **Optimism (\%)** \\ \hline
86.326 & 7.525 & 0.087 & 2.776 & 10.819 & 76.987 & 95.665 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Calculation results of the sandstone proportion of the 5 wells. \begin{table}
\begin{tabular}{c} **Standard** \\ **Error** \\ \end{tabular} & **Z-Score** \\ \hline
5 & \(-\)0.350 & \(-\)0.913 & \(-\)0.383 & \(-\)0.681 & 2.000 & 0.341 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Skewness and kurtosis normality test table. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Data Category** & **Statistics** & **DOF** & **Significance Level** \\ \hline Well data & 0.981 & 5 & 0.939 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Shapiro–Wilke (S–W) normality test table. actuality, data distribution is frequently uneven, or even only for a partial data cluster distribution, which will impact the outcome of calculations.