To calculate the Mean Absolute Deviation (MAD), we first need to understand the formula for MAD, which is defined as the average of the absolute differences between the actual values (time series values) and the forecasted values over a specified time period.
Steps to Calculate MAD:
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List the Time Series Values and Forecasts:
- Week 1: Actual = 6, Forecast = 3.00
- Week 2: Actual = 5, Forecast = 5.00
- Week 3: Actual = 4, Forecast = 5.00
- Week 4: Actual = 7, Forecast = 5.00
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Calculate the Absolute Deviations: For each week, we calculate the absolute deviation as follows: \[ \text{Absolute Deviation} = |\text{Actual} - \text{Forecast}| \]
- Week 1: \[ |6 - 3| = |3| = 3 \]
- Week 2: \[ |5 - 5| = |0| = 0 \]
- Week 3: \[ |4 - 5| = |-1| = 1 \]
- Week 4: \[ |7 - 5| = |2| = 2 \]
Summary of Absolute Deviations:
- Week 1: 3
- Week 2: 0
- Week 3: 1
- Week 4: 2
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Sum the Absolute Deviations: Now, we add up all the absolute deviations: \[ \text{Sum of Absolute Deviations} = 3 + 0 + 1 + 2 = 6 \]
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Calculate the Mean Absolute Deviation (MAD): To find the MAD, we divide the total absolute deviations by the number of observations (in this case, 4 weeks): \[ \text{MAD} = \frac{\text{Sum of Absolute Deviations}}{\text{Number of Observations}} = \frac{6}{4} = 1.5 \]
Conclusion:
Thus, the Mean Absolute Deviation (MAD) for the given time series and forecasts is: \[ \boxed{1.5} \]