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Mean Absolute Percentage Error (MAPE)

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The mean absolute percentage error (MAPE) is a measure of how accurate a forecast system is. It measures this accuracy as a percentage, and can be calculated as the average absolute percent error for each time period minus actual values divided by actual values.

Formula for Mean Absolute Percentage Error

Mean absolute percentage error (MAPE)


  • n is the number of fitted points,
  • At is the actual value,
  • Ft is the forecast value.
  • Σ is summation notation (the absolute value is summed for every forecasted point in time).

The mean absolute percentage error (MAPE) is the most common measure used to forecast error, and works best if there are no extremes to the data (and no zeros).


Beyer, W. H. CRC Standard Mathematical Tables, 31st ed. Boca Raton, FL: CRC Press, pp. 536 and 571, 2002.
Agresti A. (1990) Categorical Data Analysis. John Wiley and Sons, New York.
Dodge, Y. (2008). The Concise Encyclopedia of Statistics. Springer.
Everitt, B. S.; Skrondal, A. (2010), The Cambridge Dictionary of Statistics, Cambridge University Press.

Stephanie Glen. "Mean Absolute Percentage Error (MAPE)" From Elementary Statistics for the rest of us!

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