Methods and limitations

Mean absolute deviation

We calculate the arithmetic mean x̄ = Σxᵢ/n, then MAD = Σ|xᵢ − x̄|/n. Every observation has equal weight. This is not median absolute deviation, which is median(|xᵢ − median(x)|).

Reference: NIST: Measures of Scale.

Numeric limits

The MAD tool accepts 2–2,000 values. Nonzero magnitudes must be between 1e-12 and 1e12. Computation uses compensated summation and JavaScript double-precision numbers. It is not arbitrary-precision arithmetic. Display rounding does not change the stored calculation.

Charts and interpretation

Up to 20 values are shown as individual deviations. Larger inputs use a ten-bin histogram. The detail table and CSV retain every observation. No formal outlier test is performed.

Validation

Regression checks cover known examples, equal values, negative inputs, small values, invalid tokens and input limits. A changed calculation should pass these checks before release.