Question

Using the datga below, what is the value of the Mean absolute percent error (MAPE)?
Be sure to show your work, all inputs, calculations and explain how you arrived at your answer.
Week1,Time series value=17, Forecast=18.00
Week2,Time series value=25, Forecast=30.00
Week3,Time series value=14, Forecast=17.00
Week4,Time series value=23, Forecast=21.00

Answer 1

To calculate the Mean Absolute Percent Error (MAPE), we follow these steps:

1. **Calculate the Absolute Percentage Error for each week.**
2. **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.