Mean Absolute Deviation Calculator
Mean absolute deviation (MAD) measures the average distance of data points from the mean. Enter a comma-separated list of numbers, and the calculator displays the mean, each data point's absolute deviation, the sum of absolute deviations, and the mean absolute deviation. MAD is more robust than standard deviation when data contains outliers, as it uses absolute (not squared) deviations. This makes MAD particularly useful in data analysis involving extreme values.
Mean absolute deviation formula
mean = sum of values / N
absolute deviation = |value - mean|
MAD = sum of absolute deviations / N
Worked example
Dataset: 10, 20, 30, 40, 50
- Mean = (10 + 20 + 30 + 40 + 50) / 5 = 150 / 5 = 30
- Absolute deviations: |10-30|=20, |20-30|=10, |30-30|=0, |40-30|=10, |50-30|=20
- Sum = 20 + 10 + 0 + 10 + 20 = 60
- MAD = 60 / 5 = 12
Mean absolute deviation calculator: frequently asked questions
What is mean absolute deviation?
Mean absolute deviation (MAD) is the average distance of data points from the mean. It measures data spread using absolute (not squared) deviations. MAD = sum of |x - mean| / N. It is more interpretable than variance because it is in the same units as the original data.
How is MAD different from standard deviation?
Both measure spread, but MAD uses absolute deviations while standard deviation uses squared deviations. Squaring emphasizes outliers more heavily in standard deviation. MAD is less affected by extreme values, making it more robust for data with outliers.
When should I use MAD instead of standard deviation?
Use MAD when data has outliers that you want to minimize impact of, or when you need a more intuitive measure of average spread. Use standard deviation for normally distributed data or when statistical properties of standard deviation are needed.
What does a high MAD indicate?
High MAD means data points are far from the mean on average, indicating high variability. Low MAD means data points cluster closely around the mean, indicating low variability.
Is MAD affected by outliers?
MAD is affected by outliers less severely than standard deviation. An outlier contributes its absolute deviation (say, 50) rather than its squared deviation (2,500), making MAD more stable when extreme values are present.
Official sources
- Statistical definitions: National Institute of Standards and Technology.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.