However, when there was a large error in the raw data, the populations did become skewed, reflecting the non-linearity of the two-product formula. Figures and show the skew of the yield and recovery values respectively. When the recovery was greater than the yield, the yield values were positively skewed, meaning there was a tail of higher yield values, and on the other side of the singularity the yield values were negatively skewed with a tail of lower yield values. The opposite was the case for the recovery values. In both cases, close to the singularity the skew varied greatly in a seemingly chaotic manner. Far from the singularity the skew appears to approach a stable value, which we found scales linearly with the level of error in the raw data. Figure : Skew of the recovery values versus recovery minus yield from typical sets of N = Monte-Carlo simula ons covering a range of system yields (shown in legend), and species feed grades and recoveries, for raw assay data with rela ve errors of 10 % (RSDG = 0.10).