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Answer :
The Mean Absolute Percentage Error (MAPE) for the given data, comparing the actual values to the forecasted values, is approximately 6.69%.
To calculate the Mean Absolute Percentage Error (MAPE), we need to determine the absolute percentage error for each forecasted value and then take the average of these errors. The formula for MAPE is:
MAPE = (1/n) * Σ(|(Actual - Forecast)/Actual|) * 100
Given the actual and forecasted values:
Actual: 94, 86, 95
Forecast: 89.8, 96.8, 95.6, 96.8, 99.7, 92, 102
We can calculate the absolute percentage error for each forecasted value by subtracting the forecasted value from the actual value, taking the absolute value, dividing by the actual value, and multiplying by 100. Then, we sum up these errors and divide by the total number of forecasts.
Absolute Percentage Error for each forecast:
| (94 - 89.8) / 94 | = 0.045
| (86 - 96.8) / 86 | = 0.1279
| (95 - 95.6) / 95 | = 0.0063
| (94 - 96.8) / 94 | = 0.0298
| (95 - 99.7) / 95 | = 0.05
| (95 - 92) / 95 | = 0.0316
| (95 - 102) / 95 | = 0.0737
Sum of absolute percentage errors: 0.045 + 0.1279 + 0.0063 + 0.0298 + 0.05 + 0.0316 + 0.0737 = 0.3643
Mean Absolute Percentage Error (MAPE) = (1/7) * 0.3643 * 100 ≈ 6.69%
Therefore, the Mean Absolute Percentage Error for the given data is approximately 6.69%. This metric provides an average percentage measure of the forecast errors, indicating the overall accuracy of the forecasting model.
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