To calculate the Mean Absolute Percent Error (MAPE), we follow these steps:
- Calculate the Absolute Percentage Error for each week.
- Find the average of these absolute percentage errors.
Step 1: Calculate the Absolute Percentage Error for each week
The formula for Absolute Percentage Error (APE) for each observation is:
\[ \text{APE} = \left| \frac{\text{Actual} - \text{Forecast}}{\text{Actual}} \right| \times 100 \]
Where:
- Actual is the time series value
- Forecast is the forecasted value
Let’s calculate the APE for each week:
Week 1
- Actual = 17
- Forecast = 18.00
- APE = \(\left| \frac{17 - 18}{17} \right| \times 100 = \left| \frac{-1}{17} \right| \times 100 = 5.88%\)
Week 2
- Actual = 25
- Forecast = 30.00
- APE = \(\left| \frac{25 - 30}{25} \right| \times 100 = \left| \frac{-5}{25} \right| \times 100 = 20.00%\)
Week 3
- Actual = 14
- Forecast = 17.00
- APE = \(\left| \frac{14 - 17}{14} \right| \times 100 = \left| \frac{-3}{14} \right| \times 100 = 21.43%\)
Week 4
- Actual = 23
- Forecast = 21.00
- APE = \(\left| \frac{23 - 21}{23} \right| \times 100 = \left| \frac{2}{23} \right| \times 100 \approx 8.70%\)
Summary of Absolute Percentage Errors
- Week 1: 5.88%
- Week 2: 20.00%
- Week 3: 21.43%
- Week 4: 8.70%
Step 2: Calculate MAPE
Now we can find the Mean Absolute Percent Error (MAPE) by averaging these APEs:
\[ \text{MAPE} = \frac{\text{Sum of APEs}}{\text{Number of Weeks}} \]
Calculating the sum of APEs:
\[ \text{Sum of APEs} = 5.88 + 20.00 + 21.43 + 8.70 = 56.01% \]
Now, divide by the number of weeks (4):
\[ \text{MAPE} = \frac{56.01}{4} = 14.0025% \]
Final Result
The Mean Absolute Percent Error (MAPE) is approximately 14.00%.
Conclusion
Thus, we find that the MAPE for the provided data is 14.00%, indicating the overall forecasting accuracy expressed in percentage terms.