A time series with forecast values is presented in the following table: $$\begin{array} { | r | r | r | }
\hline \text { Month } & \text { Actual. } & \text { Forecast } \
\hline J a n & a & \
\hline \text { Mar } & 12 a & 1.1 a \
\hline \text { May} & 1.15 a & 1.2 a \
\hline J ul & 1.25 a & 12.21 a \
\hline \mathrm { Sep } & 1.3 a & 1.25 a \
\hline
\end{array}$$
If the mean absolute deviation (MAD)is 257, then a = ______.
A)4283.33
B)428.33
C)15.42
D)42.833
E)1.542

Question

A time series with forecast values is presented in the following table: $$\begin{array} { | r | r | r | } 
\hline \text { Month } & \text { Actual. } & \text { Forecast } \
\hline J a n & a & \
\hline \text { Mar } & 12 a & 1.1 a \
\hline \text { May} & 1.15 a & 1.2 a \
\hline J ul & 1.25 a & 12.21 a \
\hline \mathrm { Sep } & 1.3 a & 1.25 a \
\hline
\end{array}$$
 If the mean absolute deviation (MAD)is 257, then a = ______.
A)4283.33
B)428.33
C)15.42
D)42.833
E)1.542

Quizplus · Accepted Answer

MAD = 257 = (1/n) * sum of absolute deviationsAbsolute deviation = |Actual - Forecast|From the table, we can see that the absolute deviations are:|Actual - Forecast| = |12a - 1.1a| = 10.9a|Actual - Forecast| = |1.15a - 1.2a| = 0.05a|Actual - Forecast| = |1.25a - 12.21a| = 10.96a|Actual - Forecast| = |1.3a - 1.25a| = 0.05aSum of absolute deviations = 10.9a + 0.05a + 10.96a + 0.05a = 21.96aTherefore, 257 = (1/n) * 21.96an = 4a = 257 * 4 / 21.96a = 4283.33

A Time Series with Forecast Values Is Presented in the Following