How to use this median absolute deviation calculator
Enter your data above and press Calculate. The tool finds the median, measures every value's absolute distance from it, and returns the median of those distances, the outlier-resistant MAD.
A spread that outliers cannot bully
The median absolute deviation is built entirely from medians, and medians are famously stubborn: drag one value to a million and the MAD barely moves. That makes it the spread of choice when data is messy (sensor readings, financial returns, reaction times), anywhere a few wild points would otherwise hijack the standard deviation.
Same five values: 4, 8, 6, 10, 7. The median is 7; absolute distances from 7 are 3, 1, 1, 3, 0; the median of those is 1. Now sabotage the data: change 10 to 1000. The standard deviation explodes from 2.24 to over 400. The median absolute deviation stays exactly 1. That contrast is the entire sales pitch.
Using MAD to flag outliers
A common outlier-resistant rule converts each point's distance into "MAD units": values more than about 3.5 modified z-scores (0.6745 × distance ÷ MAD) from the median get flagged. To compare MAD with a standard deviation for roughly normal data, multiply by 1.4826, the consistency constant that makes MAD estimate the same quantity.
Frequently asked questions
What is the median absolute deviation used for?
Outlier-resistant measurement of spread and outlier detection in messy data, because it resists extreme values that would dominate the standard deviation.
How do I convert MAD to a standard-deviation-like value?
Multiply by 1.4826. For normally distributed data this scaled MAD estimates the same spread as the standard deviation.
What if the MAD is zero?
That happens when more than half the values equal the median. The dataset is extremely concentrated, or the MAD is the wrong tool for it.