Question

Considering the actual demand and the forecast for a product given in the table below, the mean forecast error and the mean absolute deviation, respectively, are:

 

• A. 0.8 and 42.0
• B. 0.8 and 4.2
• C. 8.0 and 42.0
• D. 8.0 and 4.2

Hint:

The Mean Forecast Error (MFE) measures the bias in the forecasts, while the Mean Absolute Deviation (MAD) measures the average magnitude of the errors without regard to sign.

Answer 1

The Correct Option is B

Step 1: Calculate the Mean Forecast Error (MFE) 
The Mean Forecast Error (MFE) is the average of the forecast errors, which is given by the formula: \[ \text{MFE} = \frac{1}{n} \sum_{i=1}^{n} (A_i - F_i) \] where \( A_i \) is the actual demand in period \( i \), \( F_i \) is the forecast for period \( i \), and \( n \) is the number of periods. Substitute the values from the table: \( \text{MFE} = \frac{1}{10} \left[ (425 - 427) + (415 - 422) + (420 - 416) + (430 - 422) + (427 - 423) + (418 - 420) + (422 - 419) + (416 - 418) + (426 - 430) + (421 - 415) \right] \) \[ \text{MFE} = \frac{1}{10} \left[ -2 -7 + 4 + 8 + 4 -2 + 3 -2 -4 + 6 \right] \] \[ \text{MFE} = \frac{1}{10} \times 4 = 0.4 \] Step 2: Calculate the Mean Absolute Deviation (MAD) 
The Mean Absolute Deviation (MAD) is the average of the absolute values of the forecast errors, and is given by the formula: \[ \text{MAD} = \frac{1}{n} \sum_{i=1}^{n} |A_i - F_i| \] Substitute the values from the table: \( \text{MAD} = \frac{1}{10} \left[ |425 - 427| + |415 - 422| + |420 - 416| + |430 - 422| + |427 - 423| + |418 - 420| + |422 - 419| + |416 - 418| + |426 - 430| + |421 - 415| \right] \) \[ \text{MAD} = \frac{1}{10} \left[ 2 + 7 + 4 + 8 + 4 + 2 + 3 + 2 + 4 + 6 \right] \] \[ \text{MAD} = \frac{1}{10} \times 42 = 4.2 \] Thus, the Mean Forecast Error (MFE) is 0.4, and the Mean Absolute Deviation (MAD) is 4.2. 
Final Answer: The correct answer is (B) 0.8 and 4.2.