Direct Answer
Median absolute deviation, or MAD, measures dispersion as the median of the absolute distances from the sample median. It is a robust alternative to standard deviation that ignores outliers. A larger MAD means a wider typical spread around the median.
Median Absolute Deviation: Formula, Meaning, Signals, Examples and How to Use It
How Is Median Absolute Deviation Calculated?
Median absolute deviation, or MAD, measures dispersion as the median of the absolute distances from the sample median. It is a robust alternative to standard deviation that ignores outliers.
Formula: MAD = median( |x_i - median(x)| ); a scaled version multiplies by 1.4826 to estimate standard deviation for normal data
Inputs:
- Series values
- Window length
Worked example. For the values 10, 12, 13, 15 and 40 the median is 13 and the median absolute deviation is 2.0. The inputs are illustrative numbers, not market data.
Reading it. A larger MAD means a wider typical spread around the median. It stays small even if the window contains a few extreme values, which makes it suited to noisy data with spikes.
Limits. It can be zero when more than half the values are identical, and it uses less of the data than standard deviation, so it is statistically less efficient for clean normal data.
What is Median Absolute Deviation?
Median absolute deviation, or MAD, measures dispersion as the median of the absolute distances from the sample median. It is a robust alternative to standard deviation that ignores outliers.
How to use Median Absolute Deviation
A larger MAD means a wider typical spread around the median. It stays small even if the window contains a few extreme values, which makes it suited to noisy data with spikes. A reading alone is never a buy or sell signal; it needs context from price structure, volume, volatility and the broader market regime.
Strengths
- Because medians are taken twice, up to about half of the window can be extreme values without moving the result.
- The 1.4826 scaling converts it into a standard-deviation equivalent for normal data, so it can stand in for one.
- Reproducible when the formula and data convention are fixed.
Weaknesses and limitations
- It is not additive across independent components the way variance is, so portfolio-level risk cannot be built from it.
- In a window with few distinct values the median distances take only a few levels, so the estimate moves in coarse steps.
- Correlated indicators can create false confidence by repeating the same underlying information.
Editorial and risk note
This page is educational content, not individualized investment advice. It should not imply guaranteed prediction, accuracy or outperformance.
Frequently Asked Questions
Is Median Absolute Deviation a buy or sell signal?
No. A larger MAD means a wider typical spread around the median. It can be zero when more than half the values are identical, and it uses less of the data than standard deviation, so it is statistically less efficient for clean normal data. A trade built on it still needs a trigger, an invalidation rule, a position size and realistic execution assumptions.
What is the best setting for Median Absolute Deviation?
Median Absolute Deviation takes these inputs: series values; window length. There is no universal best setting for the tunable ones, so test them across instruments, regimes and out-of-sample periods and favor stable parameter regions over one historical winner.
Can Median Absolute Deviation be used by itself?
It can be zero when more than half the values are identical, and it uses less of the data than standard deviation, so it is statistically less efficient for clean normal data. For that reason it is read next to measures of direction, participation, valuation, liquidity and risk, not alone.
Does Median Absolute Deviation work on every timeframe?
The calculation (MAD = median( |x_i - median(x)| ); a scaled version multiplies by 1.4826 to estimate standard deviation for normal data) can be run on any bar size, but behavior is not portable: a reading on a five-minute chart describes a very different market window from the same reading on a daily chart. Validate the exact timeframe before relying on it.
Why does Median Absolute Deviation give false signals?
It is not additive across independent components the way variance is, so portfolio-level risk cannot be built from it. In a window with few distinct values the median distances take only a few levels, so the estimate moves in coarse steps. Lag, noise and regime changes add to this, because market participants react to new information after the reading is calculated.
How should Median Absolute Deviation be backtested?
Rebuild Median Absolute Deviation from series values using point-in-time data, write the rules before testing, include delisted securities where relevant, model realistic fills and costs, reserve a validation sample and compare with a simpler baseline.