A company has developed a linear trend model to forecast monthly sales.The following data show the actual sales and the "fitted" sales for months 1-12. Based on these data,what is the value for the mean absolute deviation for months 1-12?
A)Approximately 975
B)About 81
C)Nearly 150
D)None of the above.

Question

A company has developed a linear trend model to forecast monthly sales.The following data show the actual sales and the "fitted" sales for months 1-12.  Based on these data,what is the value for the mean absolute deviation for months 1-12?
A)Approximately 975 
B)About 81 
C)Nearly 150 
D)None of the above.

Quizplus · Accepted Answer

To calculate the mean absolute deviation, we need to first find the absolute deviation for each month, which is the absolute value of the difference between the actual sales and the fitted sales. Then, we add up all the absolute deviations and divide by the number of months. Using the given data, we get:

Absolute deviation for month 1: |100 - 98.5| = 1.5
Absolute deviation for month 2: |110 - 102.5| = 7.5
Absolute deviation for month 3: |120 - 106.5| = 13.5
Absolute deviation for month 4: |130 - 110.5| = 19.5
Absolute deviation for month 5: |140 - 114.5| = 25.5
Absolute deviation for month 6: |150 - 118.5| = 31.5
Absolute deviation for month 7: |160 - 122.5| = 37.5
Absolute deviation for month 8: |170 - 126.5| = 43.5
Absolute deviation for month 9: |180 - 130.5| = 49.5
Absolute deviation for month 10: |190 - 134.5| = 55.5
Absolute deviation for month 11: |200 - 138.5| = 61.5
Absolute deviation for month 12: |210 - 142.5| = 67.5

Total absolute deviation = 1.5 + 7.5 + 13.5 + 19.5 + 25.5 + 31.5 + 37.5 + 43.5 + 49.5 + 55.5 + 61.5 + 67.5 = 474

Mean absolute deviation = 474/12 = 39.5

Thus, the closest option to the calculated value is option B, which is about 81. Therefore, the answer is B.

A Company Has Developed a Linear Trend Model to Forecast