Quants
Mean Absolute Deviation and Measuring Average Dispersion
When analysing data, averages alone are not enough. Two datasets can have the same mean and still behave very differently. Mean Absolute Deviation exists to address this gap. It tells us how far observations typically move away from the average, without amplifying extremes.
Rather than focusing on volatility spikes, MAD captures average inconsistency.
What Mean Absolute Deviation Really Measures
Mean Absolute Deviation measures the average distance of each observation from the mean, ignoring direction.
Each deviation is treated equally. Whether a value is above or below the mean does not matter. What matters is how far it is from the centre.
This makes MAD intuitive and easy to interpret.
Why “Absolute” Matters
If deviations were not taken in absolute terms, positive and negative differences would cancel each other out.
By using absolute values:
- all deviations contribute to dispersion
- extreme values are not exaggerated
- the measure remains linear and stable
This property distinguishes MAD from variance-based measures.
How MAD Differs from Variance and Standard Deviation
Variance and standard deviation square deviations, which gives more weight to extreme observations.
Mean Absolute Deviation does not.
As a result:
- MAD is less sensitive to outliers
- it reflects typical dispersion rather than extreme risk
- it is easier to explain conceptually
Exams often test whether candidates understand this contrast.
Interpretation in Practice
A higher Mean Absolute Deviation indicates that observations tend to be farther from the average. A lower MAD suggests values cluster more tightly around the mean.
MAD is useful when:
- distributions are not symmetric
- extreme values distort variance
- clarity is preferred over mathematical elegance
Use in Finance and Risk Analysis
In finance, MAD is sometimes used as an alternative risk measure.
It provides a sense of average deviation rather than worst-case volatility. While standard deviation remains more common, MAD helps illustrate why different risk measures exist.
Understanding this trade-off is more important than choosing one measure over another.
Limitations of Mean Absolute Deviation
MAD does not capture tail risk well.
Because it treats all deviations equally, it may understate the impact of rare but extreme outcomes. For this reason, it is often used alongside, not instead of, other dispersion measures.
Common Student Misunderstandings
Many students assume MAD and standard deviation convey the same information. They do not.
Others believe MAD is inferior because it is simpler. Simplicity is not weakness.
Some forget that MAD measures dispersion around the mean, not overall risk exposure.
These misunderstandings often appear in conceptual exam questions.
Closing Reflection
Mean Absolute Deviation offers a clean and intuitive way to think about variability. It focuses on how far values typically drift from the average without overstating extremes. For CFA and FRM preparation, the key is understanding what kind of risk MAD reflects and how it differs from variance-based measures. Once that distinction is clear, dispersion-related questions become far easier to interpret.
