Which of the following best describes the correct interpretation of $MAPE$ (Mean Absolute Percentage Error)?

• A. It is the sum of the absolute errors $|y-ŷ|$ divided by the number of observations $n$.
• B. It is the percentage of predictions that are exactly equal to the actual values.
• C. It is the average of the squared differences between predicted and actual values, i.e., $\frac{\sum {(y-ŷ)}^2}{n}$.
• D. It is the average of the absolute percentage differences between predicted and actual values, expressed as a percentage: $\frac{100}{n}\sum |\frac{y}{ŷ}-1|$.

Answer: (D)

Verified step by step guidance

1. Understand that MAPE stands for Mean Absolute Percentage Error, which is a measure used to assess the accuracy of a forecasting method.
2. Recall that MAPE calculates the average of the absolute differences between predicted values and actual values, but expressed as a percentage of the actual values.
3. Write the formula for MAPE as: \(\text{MAPE} = \frac{1}{n} \sum_{i=1}^{n} \left| \frac{A_i - F_i}{A_i} \right| \times 100\), where \(A_i\) is the actual value, \(F_i\) is the forecasted value, and \(n\) is the number of observations.
4. Note that MAPE expresses the error as a percentage, which makes it easier to interpret the size of the errors relative to the actual values.
5. Recognize that MAPE is not the sum of absolute errors, nor the percentage of exact predictions, nor the average of squared differences; it specifically measures the average absolute percentage error.