The calculation the MAD (Mean Absolute Deviation)/Mean ratio is this, according to the title: $$ \frac{\overline{\left | Forecast - Demand \right |}}{\overline{Demand}}$$ However, the calculation is often shown as this, because of the derivation from wMAPE (weighted Mean Absolute Percentage Error), with sum not average: $$ \frac{1}{\sum Demand}\sum_{}^{}Demand\frac{\left | Forecast - Demand \right |}{Demand}=\frac{\sum_{}^{}\left | Forecast - Demand \right |}{\sum_{}^{}Demand} $$ I understand why it's shown as that, because of the derivation, but that means that the title (mean) and the calculation (sum) don't match up. Are there pros and cons to using mean or sum? The key ones that I can think for using average are:
- Fair comparison between numerators and denominators of different populations, because sum is affected by number of observations
- Average is less affected by missing data than sum is, when you apply that aggregation across a column