MAD

MAD. Mean Absolute Deviation (MAD) is the median of the absolute deviations from the median of the error set. It is a dispersion measure complementary to MAE and MAPE, capturing the concentration of the error distribution rather than its central tendency.

What is MAD?

MAD is a robust dispersion measure for the per-meal error set. Computed as: MAD = median(|errors − median(errors)|). It is less sensitive to outliers than the standard deviation and complements MAE by capturing how concentrated the error distribution is.

An app with MAPE 8% and MAD 4% has errors clustered tightly around the typical 8%. An app with MAPE 8% and MAD 12% has errors that are sometimes much smaller and sometimes much larger than the typical 8%. The two distributions have the same headline MAPE but different operational implications.

When MAD is informative

MAD is informative when the question is whether the tracker is consistently mediocre (small MAD) or sometimes-very-good-and-sometimes-very-bad (large MAD). For real-world use, consistent mediocrity is often more useful than high variance — a user can plan around a tracker’s known limitation but cannot plan around unpredictable variance.

Methodology v3.2 reports MAD in supplementary tables for the keystone-review apps but not in headline figures.

Distinction from MAE

MAD and MAE are different measures. MAE is the central tendency of the absolute errors (mean). MAD is the concentration of the absolute errors around their center (median of absolute deviations from median).

For full discussion, see our metric-comparison article.