Average Absolute Error (AAE)
Always 40 units high: mean error -40.0000, AAE 40.0000. Unbiased but scattered: 0.0093 and 48.1484.
Always 40 units high: mean error -40.0000, AAE 40.0000. Unbiased but scattered: 0.0093 and 48.1484.
The median describes a typical case and cannot be summed. Both facts follow from it being a position rather than a balance point.
Means add and medians do not — which is why totals are built from means even when the median describes a typical case better.