Table 8.8
Consider the following results from the last ten periods of student enrollment forecast by the Operations Management department chairman.

Period Forecast Actual
1 25 26
2 32 31
3 42 45
4 53 50
5 64 70
6 70 72
7 81 78
8 88 90
9 95 93
10 102 105

Use Table 8.8 to determine the MAD for period 5 for the department chairman's forecast.

Question

Table 8.8
Consider the following results from the last ten periods of student enrollment forecast by the Operations Management department chairman.

Period	Forecast	Actual
1	25	26
2	32	31
3	42	45
4	53	50
5	64	70
6	70	72
7	81	78
8	88	90
9	95	93
10	102	105

Use Table 8.8 to determine the MAD for period 5 for the department chairman's forecast.

BlackTom AI · Accepted Answer

We are asked to compute the MAD for period 5 using the forecast and actual data in Table 8.8.
MAD (for periods 1 through 5) is defined as the average of the absolute differences between actual values and forecasted values for those periods.
First, list the absolute forecast errors for periods 1 to 5:
- Period 1: |Actual 26 − Forecast 25| = 1
- Period 2: |Actual 31 − Forecast 32| = 1
- Period 3: |Actual 45 − Forecast 42| = 3
- Period 4: |Actual 50 − Forecast 53| = 3
- Period 5: |Actual 70 − Forecast 64| = 6
Next, sum these absolute errors: 1 + 1 + 3 + 3 + 6 = 14.
Then divide by the number of periods considered (5) to obtain the average: 14 ÷ 5 = 2.8.
Thus, the MAD for period 5 (considering periods 1 through 5) is 2.8.
If you were to extend this to more periods, you would continue this process by including the next period’s absolute error, recomputing the average over the expanded set of periods.

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