where the summation runs over 15 thermochemical data sets. The quantity (MAE) i is the MAE for the ith data set, containing N i data points whose average absolute reference data value is |∆E| i . The total number of data points in all 15 data sets is N = i N i and |∆E| all = 56.84 kcal/mol is the average absolute reference value across all N data points. Average reference energies |∆E| i span a range from 3 kcal/mol (TAUT15) to 645 kcal/mol (DIPCS10), which is why error statistics for these myriad data sets require a weighted metric to make them comparable. It also means that the numerical value of WTMAD2 in eq. 6 should not be taken as an actual error statistic, although it does have units of energy, but instead should be used simply to rank the performance of the different functionals examined. Error statistics within each individual data sets can be found in Tables S3-S11, and the MAEs for individual data sets are provided in Fig. .