Question at position 8 Mean Absolute Deviation (MAD) Calculate the Mean Absolute Deviation (MAD) using the following data. (Refer to Slides 52, 53, and 54 in Chapter 02 -or- Pages 54 and 55 in the textbook) [table]
Month | Actual Sales | Forecast JAN | 1,345 | 1,340 FEB | 1,445 | 1,435 MAR | 1,470 | 1,460 APR | 1,390 | 1,490 MAY | 1,340 | 1,370 JUN | 1,345 | 1,350 JUL | 1,300 | 1,295 AUG | 1,375 | 1,375 SEP | 2,152 | 2,144 OCT | 2,312 | 2,296 NOV | 2,352 | 2,336 DEC | 2,224 | 2,379
[/table]AnswerMean Absolute Deviation (MAD) Calculate the Mean Absolute Deviation (MAD) using the following data. (Refer to Slides 52, 53, and 54 in Chapter 02 -or- Pages 54 and 55 in the textbook) [table]
Month | Actual Sales | Forecast JAN | 1,345 | 1,340 FEB | 1,445 | 1,435 MAR | 1,470 | 1,460 APR | 1,390 | 1,490 MAY | 1,340 | 1,370 JUN | 1,345 | 1,350 JUL | 1,300 | 1,295 AUG | 1,375 | 1,375 SEP | 2,152 | 2,144 OCT | 2,312 | 2,296 NOV | 2,352 | 2,336 DEC | 2,224 | 2,379
[/table][input]

Question

Question at position 8 Mean Absolute Deviation (MAD) Calculate the Mean Absolute Deviation (MAD) using the following data. (Refer to Slides 52, 53, and 54 in Chapter 02 -or- Pages 54 and 55 in the textbook) [table]
Month | Actual Sales | Forecast JAN | 1,345 | 1,340 FEB | 1,445 | 1,435 MAR | 1,470 | 1,460 APR | 1,390 | 1,490 MAY | 1,340 | 1,370 JUN | 1,345 | 1,350 JUL | 1,300 | 1,295 AUG | 1,375 | 1,375 SEP | 2,152 | 2,144 OCT | 2,312 | 2,296 NOV | 2,352 | 2,336 DEC | 2,224 | 2,379
[/table]AnswerMean Absolute Deviation (MAD) Calculate the Mean Absolute Deviation (MAD) using the following data. (Refer to Slides 52, 53, and 54 in Chapter 02 -or- Pages 54 and 55 in the textbook) [table]
Month | Actual Sales | Forecast JAN | 1,345 | 1,340 FEB | 1,445 | 1,435 MAR | 1,470 | 1,460 APR | 1,390 | 1,490 MAY | 1,340 | 1,370 JUN | 1,345 | 1,350 JUL | 1,300 | 1,295 AUG | 1,375 | 1,375 SEP | 2,152 | 2,144 OCT | 2,312 | 2,296 NOV | 2,352 | 2,336 DEC | 2,224 | 2,379
[/table][input]

BlackTom AI · Accepted Answer

Mean Absolute Deviation (MAD) is the average of the absolute differences between actual values and forecasts: MAD = (Σ |Actual − Forecast|) / n.

1. Relevant knowledge points and concepts
- Absolute error for each period = |Actual − Forecast|.
- MAD is the mean (arithmetic average) of those absolute errors across all periods.
- Use n = number of observations (here 12 months). Do not cancel signs (take absolute values first).

2. Complete reasoning process, step by step
- Compute the error for each month as Actual − Forecast, take its absolute value.
- Sum all absolute errors.
- Divide the sum by 12 to obtain the MAD.

3. Calculations with all intermediate steps
Month-by-month absolute errors:
- JAN: |1345 − 1340| = |5| = 5
- FEB: |1445 − 1435| = |10| = 10
- MAR: |1470 − 1460| = 10
- APR: |1390 − 1490| = |−100| = 100
- MAY: |1340 − 1370| = |−30| = 30
- JUN: |1345 − 1350| = |−5| = 5
- JUL: |1300 − 1295| = 5
- AUG: |1375 − 1375| = 0
- SEP: |2152 − 2144| = 8
- OCT: |2312 − 2296| = 16
- NOV: |2352 − 2336| = 16
- DEC: |2224 − 2379| = |−155| = 155

Sum of absolute errors = 5 + 10 + 10 + 100 + 30 + 5 + 5 + 0 + 8 + 16 + 16 + 155 = 360.

MAD = 360 / 12 = 30.0

4. Why the correct answer is correct
The MAD formula was applied exactly: each month’s error was converted to a nonnegative magnitude, summed, and averaged over the 12 months. The arithmetic yields 30.0, so the forecast’s average absolute deviation from actual sales is 30 units.

5. Common incorrect approaches (why other answers would be wrong)
- Summing signed errors (without absolute values) can cancel positive and negative errors and give an incorrectly small value (this would compute Mean Error, not MAD).
- Dividing by the wrong count (e.g., 11 instead of 12) gives an incorrect average.
- Using Forecast − Actual instead of Actual − Forecast is fine if absolute value is taken, but forgetting absolute value produces sign errors.

6. Conclusion
Following the definition and calculations above, the Mean Absolute Deviation (MAD) is 30.0, which matches the provided answer.

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