A concert promoter is forecasting this year's attendance for one of his concerts based on the following historical data: $$\begin{array} { | l | c | }
\hline { \text { Year } } & \text { Attendance } \
\hline \text { Four Years ago } & 10,000 \
\hline \text { Three Years ago } & 12,000 \
\hline \text { Two Years ago } & 18,000 \
\hline \text { Last Year } & 20,000 \
\hline
\end{array}$$
The previous trend line had predicted 18,500 for two years ago, and 19,700 for last year. What was the mean absolute deviation for these forecasts?
A) 100
B) 200
C) 400
D) 500
E) 800

Question

A concert promoter is forecasting this year's attendance for one of his concerts based on the following historical data: $$\begin{array} { | l | c | } 
\hline { \text { Year } } & \text { Attendance } \
\hline \text { Four Years ago } & 10,000 \
\hline \text { Three Years ago } & 12,000 \
\hline \text { Two Years ago } & 18,000 \
\hline \text { Last Year } & 20,000 \
\hline
\end{array}$$
The previous trend line had predicted 18,500 for two years ago, and 19,700 for last year. What was the mean absolute deviation for these forecasts?
A) 100
B) 200
C) 400
D) 500
E) 800

Quizplus · Accepted Answer

To calculate the mean absolute deviation (MAD), we first need to find the deviations between the forecasted values and the actual values from the data set. 
For two years ago, the forecasted value was off by:

| Actual attendance - Forecasted attendance |
| 18,000 - 18,500 | = 500

For last year, the forecasted value was off by:

| Actual attendance - Forecasted attendance |
| 20,000 - 19,700 | = 300

To calculate the MAD, we take the average of these two deviations:

MAD = (500 + 300)/2 = 400

Therefore, the answer is (C) 400.

A Concert Promoter Is Forecasting This Year's Attendance for One