Mad Exponential Smoothing
1. **State the problem:** We are given actual demand and forecast values for 10 weeks using exponential smoothing with $\alpha=0.60$ and initial forecast 21.0.
2. **Recall the formula for MAD (Mean Absolute Deviation):**
$$\text{MAD} = \frac{1}{n} \sum_{t=1}^n |\text{Demand}_t - \text{Forecast}_t|$$
where $n=10$ weeks.
3. **Calculate absolute errors for each week:**
- Week 1: $|21 - 21.0| = 0.0$
- Week 2: $|21 - 21.0| = 0.0$
- Week 3: $|27 - 21.0| = 6.0$
- Week 4: $|38 - 24.6| = 13.4$
- Week 5: $|25 - 32.64| = 7.64$
- Week 6: $|28 - 28.06| = 0.06$
- Week 7: $|36 - 28.02| = 7.98$
- Week 8: $|20 - 32.81| = 12.81$
- Week 9: $|25 - 25.12| = 0.12$
- Week 10: $|28 - 25.05| = 2.95$
4. **Sum the absolute errors:**
$$0 + 0 + 6 + 13.4 + 7.64 + 0.06 + 7.98 + 12.81 + 0.12 + 2.95 = 50.96$$
5. **Calculate MAD:**
$$\text{MAD} = \frac{50.96}{10} = 5.10$$
**Final answer:** The MAD for the exponential smoothing forecast is **5.10** (rounded to two decimal places).