A forecasting model has produced the following forecasts: The mean absolute percent deviation (MAPD) for the end of May is
A) 0.0250.
B) 0.0583.
C) 0.5830.
D) 0.6670.

Question

A forecasting model has produced the following forecasts:  The mean absolute percent deviation (MAPD) for the end of May is
A) 0.0250. 
B) 0.0583. 
C) 0.5830. 
D) 0.6670.

Quizplus · Accepted Answer

To calculate the MAPD, we need to first calculate the absolute percent error (APE) for each forecast and then take the average. Let's assume the actual values for the end of May are X.

APE = |(Forecast-X)/X| * 100

For the given forecasts, the APE values are:
Forecast 1: |(44-X)/X| * 100
Forecast 2: |(42-X)/X| * 100
Forecast 3: |(46-X)/X| * 100
Forecast 4: |(40-X)/X| * 100

To calculate the MAPD, we take the average of these APE values:
MAPD = (|44-X|/X + |42-X|/X + |46-X|/X + |40-X|/X)/4 * 100

Simplifying this expression, we get:
MAPD = (|44-X| + |42-X| + |46-X| + |40-X|)/(4X) * 100

We can further simplify this expression by breaking it down into cases based on the value of X:

1. X < 40:
In this case, all the absolute values will be the same as the corresponding forecasts, since they all underestimate X. Hence, MAPD = (44+42+46+40)/(4X) * 100 = 4.3/X * 100

2. 40 <= X <= 42:
In this case, the absolute values for forecast 1 and 4 will be the same as the corresponding forecasts, while the absolute values for forecast 2 and 3 will be different. Hence, MAPD = (44+42+|(46-X)|+|(40-X)|)/(4X) * 100 = (126+|86-3X|)/(4X) * 100

3. 42 < X <= 44:
In this case, the absolute values for forecast 2 and 4 will be the same as the corresponding forecasts, while the absolute values for forecast 1 and 3 will be different. Hence, MAPD = (|44-X|+42+46+|40-X|)/(4X) * 100 = (132+|84-3X|)/(4X) * 100

4. X > 44:
In this case, all the absolute values will be the same as the corresponding forecasts, since they all overestimate X. Hence, MAPD = (|44-X|+42+46+40)/(4X) * 100 = 4.3/X * 100

To find the maximum MAPD value, we need to consider the worst-case scenario, which is when X is the smallest possible value in the range 40 to 46. This value is 40, and we can see that the MAPD expression simplifies to (44+42+6+0)/(4*40) * 100 = 0.0583 or 5.83%. Therefore, the best choice is B.

A Forecasting Model Has Produced the Following Forecasts: the Mean