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What is Mean Absolute Deviation (MAD)?
Mean Absolute Deviation (MAD) is a statistical measure that quantifies the average distance between each data point and the dataset’s mean. It is used to assess variability, consistency, and forecasting accuracy.
Definition
MAD is the average of the absolute differences between each data point and the mean of the dataset.
Key Takeaways
- Measures variability in a dataset.
- Easy to compute and interpret.
- Used in statistics, forecasting, quality control, and risk analysis.
Understanding Mean Absolute Deviation (MAD)
MAD provides a clear sense of how spread out data points are. Unlike variance or standard deviation, MAD uses absolute values, which makes it less sensitive to extreme outliers.
In business forecasting, MAD is a key performance metric for evaluating forecast accuracy. Lower MAD values indicate more accurate predictions.
MAD is also useful in identifying data consistency, quality variations, and distribution patterns.
Formula (If Applicable)
If a dataset has values (x_1, x_2, …, x_n) with mean (\bar{x}):
[ \text{MAD} = \frac{1}{n} \sum_{i=1}^{n} |x_i – \bar{x}| ]
Real-World Example
A retail company evaluates the accuracy of its weekly sales forecasts. If the actual and forecasted values differ by an average of 150 units, the MAD is 150. Lower MAD helps improve inventory and planning decisions.
Importance in Business or Economics
MAD is essential for forecasting accuracy, financial modelling, operational planning, and quality management. It simplifies variability analysis and supports better decision-making.
Types or Variations
- Mean Absolute Error (MAE)
- Median Absolute Deviation
- Standard Deviation (related measure)
Related Terms
- Variance
- Standard Deviation
- Forecast Error
Sources and Further Reading
- Investopedia – Mean Absolute Deviation
- Penn State – Statistical Concepts
- NIST – Data Variability
Quick Reference
- Average absolute deviation from the mean.
- Indicates variability and forecasting accuracy.
- Less sensitive to outliers than standard deviation.
Frequently Asked Questions (FAQs)
Is MAD better than standard deviation?
It depends, MAD is easier to interpret and less affected by outliers.
Can MAD be zero?
Yes, only when all data points are identical.
Is MAD used in forecasting?
Yes, it is a popular error metric for evaluating forecast accuracy.
