Mean absolute deviation

Mean absolute deviation (MAD) is a statistical measure of forecast error calculated as the average of the absolute differences between forecasted values and actual values, providing a simple and intuitive assessment of forecast accuracy (Stevenson W.J. 2018, p.82)^[1]. You predicted 100 units; actual demand was 90. The error is 10. Tomorrow you predicted 150; actual was 165. Error: 15. Average those absolute errors over many periods and you have MAD. It tells you, on average, how far off your forecasts are—without caring whether you over- or under-predicted.

MAD is widely used in demand planning, inventory management, and operations because it's easy to calculate and interpret. Unlike measures that square errors, MAD uses the same units as the data itself. If you're forecasting widgets, MAD is in widgets. That directness makes it accessible to practitioners who need to understand forecast quality without statistical sophistication.

Calculation

The formula is straightforward:

Basic formula

MAD = Σ|Actual - Forecast| / n. Sum the absolute values of all forecast errors, then divide by the number of observations^[2].

Step-by-step

1. Calculate errors. For each period, subtract the forecast from the actual value.

2. Take absolute values. Convert negative errors to positive—we care about magnitude, not direction.

3. Sum. Add all absolute errors together.

4. Average. Divide by the number of periods to get the mean.

Example

| Period | Forecast | Actual | Error | Absolute Error | |--------|----------|--------|-------|----------------| | 1 | 100 | 90 | -10 | 10 | | 2 | 150 | 165 | 15 | 15 | | 3 | 200 | 195 | -5 | 5 | | 4 | 180 | 200 | 20 | 20 |

MAD = (10 + 15 + 5 + 20) / 4 = 12.5

The forecast is off by an average of 12.5 units per period^[3].

Interpretation

Understanding what MAD tells you:

Direct meaning

Average error magnitude. MAD represents the expected absolute error of a forecast. A MAD of 50 means forecasts typically miss by about 50 units.

Same units. Unlike squared-error measures, MAD is expressed in the same units as the forecast, making interpretation intuitive.

Comparing methods

Lower is better. When comparing forecasting methods, the one with the smallest MAD has generally produced more accurate forecasts over the measured period^[4].

Method selection. Organizations often test multiple forecasting approaches on historical data and select the one with the lowest MAD.

Advantages

MAD offers several benefits:

Simplicity. Easy to calculate without specialized software or statistical expertise.

Interpretability. The result is intuitive—it's the average miss in natural units.

Robustness. Because MAD doesn't square errors, it's less sensitive to outliers than mean squared error^[5].

Practical relevance. MAD directly relates to inventory and operational decisions. An average error of 50 units has practical meaning.

Limitations

MAD has weaknesses:

No direction information

Bias blindness. MAD treats over-forecasting and under-forecasting the same. A consistent 10% over-forecast produces the same MAD as 10% under-forecast, but the operational implications differ.

Tracking signal. Supplementing MAD with bias measures helps detect systematic over- or under-forecasting.

Scale dependence

Volume effects. MAD is not comparable across products with different volumes. A MAD of 50 on a product averaging 100 units is worse than MAD of 50 on a product averaging 1,000 units^[6].

Percentage measures. MAPE (mean absolute percentage error) addresses this by expressing error as a percentage.

Outlier sensitivity

Large errors. While less sensitive than squared measures, MAD still includes all errors equally. A few extreme misses raise the average.

Related measures

MAD exists within a family of accuracy measures:

Mean squared error (MSE)

Squared errors. MSE squares each error before averaging, giving more weight to large errors. Useful when large errors are especially problematic.

Root mean squared error (RMSE)

Square root of MSE. Returns to original units by taking the square root of MSE. More sensitive to outliers than MAD^[7].

Mean absolute percentage error (MAPE)

Percentage basis. Expresses errors as percentages of actual values, enabling comparison across products with different scales.

Tracking signal

Bias detection. Cumulative error divided by MAD indicates whether the forecast consistently over- or under-predicts.

Applications

MAD serves practical purposes:

Forecast method selection. Compare MAD across methods to choose the most accurate.

Safety stock calculation. MAD informs safety stock decisions—higher MAD suggests higher safety stock needed^[8].

Supplier evaluation. Vendors' forecast accuracy can be assessed using MAD.

Continuous improvement. Tracking MAD over time reveals whether forecast accuracy is improving.

Mean absolute deviation — recommended articles

Forecasting — Statistics — Inventory management — Operations management

References

• Stevenson W.J. (2018), Operations Management, 13th Edition, McGraw-Hill.
• Hyndman R.J., Athanasopoulos G. (2021), Forecasting: Principles and Practice, 3rd Edition, OTexts.
• Oracle (2023), Mean Absolute Deviation.
• Real Statistics (2023), Forecast Error Measures.

Footnotes

1. ↑ Stevenson W.J. (2018), Operations Management, p.82
2. ↑ Hyndman R.J., Athanasopoulos G. (2021), Forecasting, Chapter 5
3. ↑ Oracle (2023), MAD Calculation
4. ↑ Stevenson W.J. (2018), Operations Management, pp.94-106
5. ↑ Real Statistics (2023), Forecast Error Measures
6. ↑ Hyndman R.J., Athanasopoulos G. (2021), Forecasting, Chapter 5.3
7. ↑ Stevenson W.J. (2018), Operations Management, pp.112-118
8. ↑ Oracle (2023), Safety Stock Calculations

Author: Sławomir Wawak