A demand model has these errors on 5 held-out weeks (actual − predicted): +10, −10, +20, −20, +100 units.
What are the MAE and the RMSE, and what does the difference tell you?
Why did you pick that answer? Two or three sentences. The act of articulating it is what builds the judgment — not the click that follows.
MAE = (10 + 10 + 20 + 20 + 100) / 5 = 32. RMSE = √((100 + 100 + 400 + 400 + 10,000) / 5) = √2,200 ≈ 46.9 → about 47. Because squaring magnifies large errors, RMSE ≥ MAE always, and the gap grows with outliers. If a single stockout week is very costly, RMSE is the metric that reflects it; if every unit of error costs the same, report MAE.
They agree only when every error has the same size. Here one error is ten times the others, so RMSE is pulled up.
Both metrics use absolute or squared errors precisely so that positive and negative misses cannot cancel.
The square root undoes the squaring only on average; the large error still dominates the sum inside the root.