Which metric expresses error as a percentage of actual values?

Which metric expresses error as a percentage of actual values?

• A. MAPE
• B. MSE
• C. RMSE
• D. MAE

Answer: (A)

The key idea is measuring how large the forecasting error is relative to what actually happened, i.e., a relative, percent-based error. This is exactly what mean absolute percentage error captures: it takes the absolute difference between each actual value and its forecast, divides by the actual value, averages these percentages, and expresses the result as a percentage. MAPE = (1/n) sum over observations of |actual − forecast| / actual × 100. This makes the metric intuitive to compare across different scales, because you’re looking at the error as a share of what was observed. For example, an absolute error of 20 units is far more meaningful when actual values are around 20 than when they’re around 1000; MAPE puts that into perspective by converting to a percentage. In contrast, the other common metrics aren’t percentages: mean squared error and its square root are in units tied to the target (squared units or the same units as the target, respectively), and mean absolute error is an average of absolute differences in the same units as the target. So they don’t express error as a percentage of the actual values. One caveat: MAPE can be problematic when actual values are zero or near zero, since dividing by a small actual inflates the percentage error. Still, when you want error expressed as a percentage of what was actually observed, MAPE is the best fit.

The key idea is measuring how large the forecasting error is relative to what actually happened, i.e., a relative, percent-based error. This is exactly what mean absolute percentage error captures: it takes the absolute difference between each actual value and its forecast, divides by the actual value, averages these percentages, and expresses the result as a percentage.

MAPE = (1/n) sum over observations of |actual − forecast| / actual × 100.

This makes the metric intuitive to compare across different scales, because you’re looking at the error as a share of what was observed. For example, an absolute error of 20 units is far more meaningful when actual values are around 20 than when they’re around 1000; MAPE puts that into perspective by converting to a percentage.

In contrast, the other common metrics aren’t percentages: mean squared error and its square root are in units tied to the target (squared units or the same units as the target, respectively), and mean absolute error is an average of absolute differences in the same units as the target. So they don’t express error as a percentage of the actual values.

One caveat: MAPE can be problematic when actual values are zero or near zero, since dividing by a small actual inflates the percentage error. Still, when you want error expressed as a percentage of what was actually observed, MAPE is the best fit.