## 5 Statistical Analysis of the Dataset  
In order to provide a first glimpse of the collected data, Table 3 presents a comprehensive overview of the dataset through key statistical indices for each field: minimum, maximum, and mean value, standard deviation, and 25 th-50 th-75 th percentiles. In addition to the dimensions already presented in Table 1, the list includes the number of spare processes (i.e., the number of additional ranks necessary to provide fault tolerance), the total number of processes, the number of processes assigned to each socket (directly connected to the aforementioned \"span\" or \"fill\" policy for rank assignment), ScaLAPACK blocking factor and checkpointing rate, and four key metrics related to each job run: total energy consumption, peak power, average power, and execution time. Focusing on the latter four metrics, Table 3 suggests that, in the proposed dataset, the total energy and runtime metrics have high variability, as indicated by their large standard deviations and the extensive range between the minimum and maximum values. Also, the median values are much lower than the mean, indicating that a significant number of jobs have energy and runtime values lower than the mean, but a few jobs increase the average. On the contrary, peak and average power consumption seem more uniformly distributed, with median values more similar to the mean ones. Figure 3 presents histograms for energy, runtime, peak, and average power consumption metrics, showing the general shape of the data distributions when considering the whole dataset samples. So, for example, the energy graph reports different ranges of energy consumed on the \(x\) axis, and the height of the bars indicates the number of samples (i.e., job runs present in the dataset) that fall into the corresponding energy range. Above the histograms, a density curve estimates the variable's probability distribution. Given \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Fields\_Index** & **Mean** & **Std** & **Min** & **25\%** & **50\%** & **75\%** & **Max** \\ \hline _Matrix size_ & 22,176 & 11,760.75 & 5280 & 10,560 & 21,120 & 31,680 & 42,240 \\ \hline _Calculation_ & 314 & 181.084 & 64 & 144 & 256 & 484 & 576 \\ \hline _Spare processes_ & 29.73 & 45.73 & 0 & 2 & 8 & 40 & 192 \\ \hline _Total processes_ & 343.73 & 195.41 & 64 & 148 & 320 & 492 & 768 \\ \hline _Nodes_ & 7.67 & 4.02 & 2 & 4 & 7 & 11 & 16 \\ \hline _Fault tolerance level_ & 3.33 & 2.7 & 0 & 1 & 2 & 4 & 8 \\ \hline _Simulated faults_ & 1.67 & 2.58 & 0 & 0 & 0 & 2 & 8 \\ \hline _Processes per socket_ & 10.99 & 11.11 & 0 & 0 & 8 & 23 & 24 \\ \hline _ScaLAPACK_ & 4928 & 6762.64 & 0 & 0 & 0 & 10,560 & 21,120 \\ _checkpoint_ & 10.38 & 11.63 & 0 & 0 & 0 & 24 & 25 \\ \hline _Total energy (Wh)_ & _77.73_ & 144.39 & 0.73 & 6.88 & 17.69 & 69.4 & 2626.28 \\ \hline _Peak power (W)_ & 2131.32 & 1195.63 & 280 & 1120 & 1900 & 3030 & 5700 \\ \hline _Average power (W)_ & 1960.72 & 1064.42 & 304 & 990.10 & 1835.87 & 2813.40 & 4879.89 \\ \hline _Runtime (s)_ & 142.07 & 282.77 & 6 & 15 & 36 & 129.75 & 9481 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Description of the dataset data. the skewed nature of energy and runtime data deducible from the values in Table 3, these two metrics are presented in a logarithmic scale to better appreciate their trends. Besides an unusual, non-strict correlation between runtime and energy consumed, the graphs suggest that the average value of the system power follows a similar trend to that of the maximum system power. However, if we restrict our attention to different dataset slices, other trends emerge. For example, Figure 4 focuses on a subset of job runs involving just 2, 8, or 16 physical nodes.