Using the data below, what is the value of MAD?

Question

Week1, Time Series Value=6, Forecast=8.00
Week2, Time Series Value=5, Forecast=2.00
Week3, Time Series Value=4, Forecast=3.00
Week4, Time Series Value=7, Forecast=5.00

Answer 1

To calculate the Mean Absolute Deviation (MAD), you first need to find the absolute deviations for each week, and then average these absolute deviations.

The formula for the absolute deviation for each week is:

\[ \text{Absolute Deviation} = |\text{Time Series Value} - \text{Forecast}| \]

Now, let's calculate the absolute deviations for each week:

1. Week 1: \[ |6 - 8.00| = | -2 | = 2 \]

2. Week 2: \[ |5 - 2.00| = | 3 | = 3 \]

3. Week 3: \[ |4 - 3.00| = | 1 | = 1 \]

4. Week 4: \[ |7 - 5.00| = | 2 | = 2 \]

Now, let's sum these absolute deviations:

\[ \text{Total Absolute Deviation} = 2 + 3 + 1 + 2 = 8 \]

Next, we calculate the MAD by dividing the total absolute deviation by the number of weeks (n = 4):

\[ \text{MAD} = \frac{\text{Total Absolute Deviation}}{n} = \frac{8}{4} = 2 \]

Therefore, the value of the Mean Absolute Deviation (MAD) is 2.