1. **Stating the problem:** We have actual sales and two forecast methods (M1 and M2) for 6 days. We need to calculate: - Method 1's MAD (Mean Absolute Deviation) - Method 2's MAD - Method 1's MAPE (Mean Absolute Percentage Error) - Method 2's MAPE 2. **Formulas:** - MAD = $\frac{1}{n} \sum_{i=1}^n |\text{Actual}_i - \text{Forecast}_i|$ - MAPE = $\frac{100}{n} \sum_{i=1}^n \left| \frac{\text{Actual}_i - \text{Forecast}_i}{\text{Actual}_i} \right|$ 3. **Calculate absolute errors for each day:** | Day | Actual | M1 Forecast | M1 Error $|Actual - M1|$ | M2 Forecast | M2 Error $|Actual - M2|$ | |----------|--------|-------------|---------------------|-------------|---------------------| | Monday | 14 | 12 | 2 | 13 | 1 | | Tuesday | 30 | 34 | 4 | 32 | 2 | | Wednesday| 24 | 24 | 0 | 28 | 4 | | Thursday | 29 | 26 | 3 | 28 | 1 | | Friday | 13 | 16 | 3 | 17 | 4 | | Saturday | 14 | 11 | 3 | 12 | 2 | 4. **Calculate MAD:** - M1 MAD = $\frac{2+4+0+3+3+3}{6} = \frac{15}{6} = 2.50$ - M2 MAD = $\frac{1+2+4+1+4+2}{6} = \frac{14}{6} \approx 2.33$ 5. **Calculate percentage errors for MAPE:** | Day | M1 Percentage Error $\left|\frac{Actual - M1}{Actual}\right| \times 100$ | M2 Percentage Error $\left|\frac{Actual - M2}{Actual}\right| \times 100$ | |----------|-------------------------------------------------------------|-------------------------------------------------------------| | Monday | $\frac{2}{14} \times 100 \approx 14.29\%$ | $\frac{1}{14} \times 100 \approx 7.14\%$ | | Tuesday | $\frac{4}{30} \times 100 \approx 13.33\%$ | $\frac{2}{30} \times 100 \approx 6.67\%$ | | Wednesday| $\frac{0}{24} \times 100 = 0\%$ | $\frac{4}{24} \times 100 \approx 16.67\%$ | | Thursday | $\frac{3}{29} \times 100 \approx 10.34\%$ | $\frac{1}{29} \times 100 \approx 3.45\%$ | | Friday | $\frac{3}{13} \times 100 \approx 23.08\%$ | $\frac{4}{13} \times 100 \approx 30.77\%$ | | Saturday | $\frac{3}{14} \times 100 \approx 21.43\%$ | $\frac{2}{14} \times 100 \approx 14.29\%$ | 6. **Calculate MAPE:** - M1 MAPE = $\frac{14.29 + 13.33 + 0 + 10.34 + 23.08 + 21.43}{6} \approx \frac{82.47}{6} = 13.75\%$ - M2 MAPE = $\frac{7.14 + 6.67 + 16.67 + 3.45 + 30.77 + 14.29}{6} \approx \frac{78.99}{6} = 13.17\%$ **Final answers:** - Method 1's MAD = 2.50 - Method 2's MAD = 2.33 - Method 1's MAPE = 13.75% - Method 2's MAPE = 13.17%