Mean Absolute Percentage Error (MAPE) is a statistical measure that evaluates the accuracy of a forecasting or predictive model. It calculates the average of the absolute percentage errors between predicted values and actual values. MAPE expresses forecast error as a percentage of the actual values, making it easy to interpret and compare across different datasets or units. Analysts commonly use MAPE in fields such as finance, retail, supply chain management, and energy forecasting to assess how closely model predictions match observed outcomes.
The formula for calculating MAPE is:
MAPE = (1/n) × Σ(|Actual – Predicted| / Actual) × 100
This formula calculates the absolute difference between actual and predicted values for each observation, divides that difference by the actual value to express it as a percentage, and then averages these percentages across all observations. The result is a single percentage that reflects the typical size of prediction errors relative to actual values.
For example, suppose a retail analyst is forecasting weekly sales of a product and compares actual sales with predicted sales for four weeks:
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Week 1: Actual = 100, Predicted = 110
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Week 2: Actual = 150, Predicted = 140
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Week 3: Actual = 120, Predicted = 115
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Week 4: Actual = 130, Predicted = 125
The absolute percentage errors for each week are: 10%, 6.67%, 4.17%, and 3.85%. The MAPE would be the average of these values:
MAPE = (10 + 6.67 + 4.17 + 3.85) / 4 = 6.67%
This result means the analyst’s forecast was off by about 6.67% on average.
One important limitation of MAPE is that it can become distorted or undefined when any actual values are zero, since the formula divides by the actual value. Even very small actual values can cause the percentage error to spike, exaggerating the impact of relatively small prediction errors. For this reason, MAPE may not be appropriate when the dataset includes zero or near-zero actual values. In such cases, alternative measures like SMAPE (Symmetric Mean Absolute Percentage Error) or MAE (Mean Absolute Error) may offer more stable and interpretable results.
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