## 3 Results
### Assessing the Distribution and Spread of Simulated Grades  
Commonly, in assessing the consistency of an assessment method, it is asserted that individual student grades follow a normal distribution [17; 18]. Figure 2 displays the fitting results of a normal distribution to grading data simulated using the Summative, Rubric, ST, and ST-FIS methods. Table 8 includes fitting statistics. The histograms are displayed in Figure 2. Entries in Table 8 show consistent fittings in all cases. Table 8 presents the results of normal distribution fits to student grades generated using different assessment methods: Summative, Rubric, ST, and ST-FIS. Regarding the Mean and Standard Deviation, the Rubric method had the highest mean score (0.5874), indicating that students tend to score higher under this method compared to the others. The Summative method yielded a mean of 0.5214, which is slightly lower than the Rubric method. The ST method yielded a similar mean value (0.5044), indicating comparable grading outcomes to those of the Summative. The ST-FIS method had a slightly lower mean of (0.4982). Comparing standard deviation values, the smallest one was linked to the ST method (0.0697), indicating that this scheme has the lowest variability, meaning that the produced students' grades are more clustered around the mean. The ST-FIS method reported a standard deviation of (0.2463), implying that this scheme shows a wider variability in student grades around the mean. The Summative approach reported a value of 0.1412, only slightly different from the one for the Rubric scheme (0.1410). Therefore, the spreads of grades produced by these last methods around the mean could be considered equivalent. Regarding goodness of fit, we relied on Chi-squared statistics that evaluate how well the normal distribution fits the data. Lower values indicate a better fit. The degrees of freedom (df) associated with each \(\chi^{2}\) test included in Table 8 allow for full interpretation of the \(p\)-values. Reported \(p\)-values reflect the probability of observing the test statistics under \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Mean**} & **Standard** & **Chi-Squared** & **Degrees of** & \multirow{2}{*}{_p-Value_} \\  & & **Deviation** & **Statistic** & **Freedom** & \\ \hline Summative & 0.5214 & 0.1412 & 1.0663 & 2 & 0.5868 \\ Rubric & 0.5874 & 0.1410 & 3.1181 & 3 & 0.3738 \\ ST & 0.5044 & 0.0697 & 1.3905 & 3 & 0.7078 \\ ST-FIS & 0.4982 & 0.2463 & 3.5090 & 2 & 0.1730 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results of normal distribution fitting to simulated student grades, based on the provided mathematical setups, incorporating the Summative, Rubric, ST, and ST-FIS methods. Figure 2: Normal distribution fitting to simulated grade data. Panel (**a**) shows the Summative method, in which the fit of a normal distribution to simulated grades is acceptable (failing to reject H0). Panel (**b**) fits a normal distribution to a Rubric method’s simulated scores; the fit is appropriate (failing to reject H0). Panel (**c**) shows the fit of a normal distribution to simulated grade data using the ST scheme. The fit is satisfactory (failing to reject H0). Panel (**d**) shows the fit of a normal distribution to grading data simulated according to the ST-FIS method; the fit is also acceptable (i.e., we fail to reject H0). the null hypothesis that the data follow a normal distribution. While the simulated grade data generated by the proposed assessment methods generally fit a normal distribution well (as the high \(p\)-values indicate), as we have emphasized, real-world grading data may not always exhibit this behavior. Therefore, the assumption of normality in this context serves as a controlled benchmark for evaluating whether our simulation procedures produce well-centered and symmetric grade outcomes under ideal conditions. It is not intended to generalize to all educational contexts but to support internal consistency analysis among the compared methods.