What Does MAD Mean in Math?
n math and statistics, MAD usually means Mean Absolute Deviation or Median Absolute Deviation, depending on the context. Mean Absolute Deviation measures the average distance between each value in a dataset and the arithmetic mean. Median Absolute Deviation is a different statistic that uses the median and is more resistant to outliers.
On this page, MAD means Mean Absolute Deviation from the arithmetic mean.
How to Find the MAD of a Data Set
To find the Mean Absolute Deviation (MAD) of a data set:
- Find the arithmetic mean of the data.
- Find the distance from the mean for each value by subtracting the mean from each value.
- Take the absolute value of each difference so all distances are positive.
- Add the absolute deviations together.
- Divide the total by the number of values in the data set.
Mean Absolute Deviation Formula
MAD = (1/n) × Σ |xᵢ − x̄| Where x̄ is the arithmetic mean of the dataset, xᵢ is each individual value, and n is the number of values.
Mean Absolute Deviation, not Median Absolute Deviation
This calculator measures Mean Absolute Deviation from the arithmetic mean — not Median Absolute Deviation. "MAD" is a genuinely ambiguous abbreviation: it's used for both statistics, and they can give very different numbers for the same dataset. Median Absolute Deviation replaces both the central point and the averaging step with medians instead of means, which makes it far less sensitive to extreme values (outliers). Mean Absolute Deviation, the statistic this calculator computes, uses the mean throughout, which makes it more directly comparable to other mean-based statistics like standard deviation — but also more affected by outliers, the same way the mean itself is.
For example, take the dataset 1, 2, 3, 4, 100:
- Mean Absolute Deviation (from the mean): 31.2
- Median Absolute Deviation (a different statistic, not computed here): 1
The single outlier value (100) pulls the mean sharply upward, which pulls Mean Absolute Deviation up with it. Median Absolute Deviation barely moves, because the median itself barely moves when one value in a small dataset is extreme. Neither number is "wrong" — they're answering the same general question (how spread out is this data?) with different sensitivity to extreme values, which is exactly why it matters which one a calculator, or a textbook problem, actually means by "MAD."
Worked example
For the dataset 2, 4, 6, 8, 10:
- Mean: (2 + 4 + 6 + 8 + 10) ÷ 5 = 6
- Absolute deviations from the mean: 4, 2, 0, 2, 4
- Mean Absolute Deviation: (4 + 2 + 0 + 2 + 4) ÷ 5 = 2.4
Frequently asked questions
Is Mean Absolute Deviation the same as mean deviation?
Mean deviation is often used as another name for Mean Absolute Deviation, particularly when the deviations are measured from the arithmetic mean. The exact terminology can vary by textbook or course.
Why isn't this calculator's result matching my textbook's "MAD" answer?
Double-check which statistic your textbook or course actually means by "MAD." Some courses (particularly in robust statistics) use "MAD" to mean Median Absolute Deviation, a different calculation that uses the median instead of the mean at both steps. This calculator computes Mean Absolute Deviation from the arithmetic mean specifically, which is the more common meaning in introductory statistics but not the only one in use.
How is Mean Absolute Deviation different from standard deviation?
Both measure spread around the mean, but standard deviation squares each deviation before averaging (then takes a square root at the end), while Mean Absolute Deviation just takes the absolute value. Squaring weights larger deviations more heavily, which is why standard deviation tends to be more sensitive to outliers than Mean Absolute Deviation.
How do you find MAD?
To find Mean Absolute Deviation, first calculate the arithmetic mean. Find the absolute difference between each value and the mean, add those differences, and divide by the number of values.
What does MAD stand for in math?
In statistics, MAD can mean Mean Absolute Deviation or Median Absolute Deviation. This calculator uses Mean Absolute Deviation, which is the average absolute distance of the data values from their arithmetic mean.