Understand the statistic
Measuring how observations vary. Spread describes how tightly or widely values lie around a reference. It complements a center: two datasets can share the same mean while behaving very differently.
1Locate the reference center2Measure each observation’s distance3Combine distances using the displayed rule
Calculation rule
MAD = median(|xᵢ−median(x)|); normal-consistent MAD = MAD/Φ⁻¹(0.75).
The formula is applied only to the observations and options you enter. No population, distribution, or sampling process is inferred automatically.
How to read the answer
MAD resists a small number of extreme observations, making it useful beside—not automatically instead of—standard deviation.
Important: The 1.4826 scaling is a normal-model consistency convention; it does not make non-normal data normal.
Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the median absolute deviation calculator works
MAD = median(|xᵢ−median(x)|); normal-consistent MAD = MAD/Φ⁻¹(0.75).
MAD resists a small number of extreme observations, making it useful beside—not automatically instead of—standard deviation.
Worked example
Median Absolute Deviation example
For 1, 2, 2, 3, 100, the median is 2 and the raw MAD is 1 despite the extreme final value.
MAD = median(|xᵢ−median(x)|); normal-consistent MAD = MAD/Φ⁻¹(0.75).
Supported inputs
Precision and limits
Model and design
The 1.4826 scaling is a normal-model consistency convention; it does not make non-normal data normal.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
MAD resists a small number of extreme observations, making it useful beside—not automatically instead of—standard deviation.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
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