A retailer reports forecast error as MAPE. Last week, one new product sold 2 units against a forecast of 12; a best-seller sold 1,000 against a forecast of 1,100.
What is each product's absolute percentage error, and what does this expose about MAPE?
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.
APE = |actual − forecast| / actual: |2 − 12| / 2 = 500% for the new product, |1,000 − 1,100| / 1,000 = 10% for the best-seller. Averaging those gives 255% — driven almost entirely by an item that missed by 10 units. MAPE explodes near zero and weights every product equally regardless of revenue. Weighted MAPE (errors summed over volume) or MAE in units are the usual fixes.
Dividing by the forecast instead of the actual is a different metric. Standard MAPE divides by the actual value.
10 / 12 = 83% uses the forecast as the base. Standard MAPE uses actuals — and the point is that 500% is absurd for a 10-unit miss.
Those are absolute errors in units (MAE). MAPE converts them to percentages, which is exactly where the distortion enters.