Median Absolute Deviation Calculator — Robust Spread Measure
Enter a list of numbers and get the median absolute deviation (MAD) — the median of how far each value sits from the dataset median — along with the robust standard deviation estimate, mean, and population standard deviation.
Median of |xᵢ − median| — a robust spread measure
- 1
Median of dataset
4.5The middle value of the sorted data; used as the center for computing deviations. - 2
MAD = median(|xᵢ − median|)
median(|xᵢ − 4.5|) = 0.5000
How does this calculator work?
Median Absolute Deviation = median(|xᵢ − median(x)|). Compute the median, find each value's absolute distance from it, then take the median of those distances. For normally distributed data, MAD ≈ 0.6745 σ, so divide by 0.6745 for a robust σ estimate. MAD resists outliers better than standard deviation.
Formula
How this is calculated
The median absolute deviation (MAD) measures spread by centering on the median rather than the mean. First the median of all values is found. Then the absolute deviation of each value from that median is computed: |xᵢ − median|. Finally, the median of those absolute deviations is taken — that is the MAD.
MAD is more robust than the standard deviation or the mean absolute deviation (MAD from the mean) because both the center and spread are computed using medians, which are unaffected by a small fraction of extreme outliers. Under a normal distribution, the relationship MAD ≈ 0.6745 × σ holds, so dividing MAD by 0.6745 gives a robust estimate of the population standard deviation σ — useful when you suspect contamination or heavy tails.
The calculator also reports the arithmetic mean and population standard deviation (σ, dividing by n) for comparison. When the data is symmetric and outlier-free the two spread measures agree closely; a large gap between MAD/0.6745 and σ is a signal that outliers or skewness are inflating the classical deviation.
Frequently asked questions
This calculator computes the median of |xᵢ − median|, which is the classic "Median Absolute Deviation." Some sources instead compute the mean of |xᵢ − mean|, which is sometimes called "Mean Absolute Deviation." Both use "MAD" as an abbreviation, but the median-based version is the more robust of the two.
Under a normal distribution, the expected MAD equals 0.6745 σ. Dividing by this factor re-scales MAD to be a consistent estimator of σ. The scaling factor (Φ⁻¹(3/4) ≈ 0.6745) comes from the inverse normal CDF at the 75th percentile.
Use MAD when your data may contain outliers or is from a heavy-tailed distribution. It is popular in robust statistics, anomaly detection, and fields such as finance where extreme values are common but should not dominate the spread measure.
Also known as
TG we-Calculate Editorial Team. (2026). Median Absolute Deviation Calculator — Robust Spread Measure [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/median-absolute-deviation-calculator
TG we-Calculate Editorial Team. "Median Absolute Deviation Calculator — Robust Spread Measure." TG we-Calculate. 2026. https://we-calculate.com/calculator/median-absolute-deviation-calculator.
TG we-Calculate Editorial Team, "Median Absolute Deviation Calculator — Robust Spread Measure," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/median-absolute-deviation-calculator
@misc{wecalculate_median_absolute_deviation_calculator, title = {Median Absolute Deviation Calculator — Robust Spread Measure}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/median-absolute-deviation-calculator}}, year = {2026}, note = {TG we-Calculate} }
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