Distinguish Raw and Scaled Median Absolute Deviation

State which spread measure you mean

Median absolute deviation, often abbreviated MAD, starts with the median of the observations. Calculate each observation's absolute distance from that median, then take the median of those distances. It differs from the mean absolute deviation and from the standard deviation, even though all describe spread.

The official R MAD documentation explains both the raw calculation and the default scaling factor of 1.4826. That factor supports comparison with the SD under a normal-distribution reference; it does not turn every dataset into normally distributed data.

Preserve the population and units

Record the outcome, measurement window, units, and eligible observations before summarizing. Check special missing codes, repeated measurements, and whether the data are genuinely numerical. The median of a set of arbitrary category identifiers is not a meaningful substitute for a categorical summary.

Decide how missing observations will be reported. A robust summary can be less sensitive to some extreme values than an SD, but it does not solve informative missingness, biased sampling, or systematic measurement error. Keep the observed count and missing count visible.

Work through a fictional calculation

For fictional values 1, 2, 3, 4, and 9, the median is 3. Absolute deviations are 2, 1, 0, 1, and 6. Ordered deviations are 0, 1, 1, 2, and 6, so raw MAD is 1. Multiplying by 1.4826 gives scaled MAD 1.4826.

Changing the final value from 9 to 90 leaves these two MAD summaries unchanged. This illustrates their limited sensitivity to that single change, not permission to ignore the observation. The maximum, range, and other features of the data change substantially and still deserve inspection.

Interpret a small or zero result carefully

The rank-summary tool reports raw MAD only, without the 1.4826 scaling. The scaled value above is a separate illustration of a convention used by some software. Record the selected convention in the descriptive-summary plan; a table labeled only “MAD” may otherwise be ambiguous to another analyst.

Tied observations can produce MAD zero even when some values differ. For instance, 2, 2, 2, 2, and 10 have median 2 and raw MAD zero. That does not mean every observation equals two or that the instrument has perfect precision. Inspect the frequency distribution before using MAD in a denominator or an outlier rule.

Use plots and source checks to investigate unusual observations rather than automatically deleting them. If the analysis plan uses a robust summary, explain why that choice fits the question and report its definition consistently across groups. Finish with the median, clearly labeled spread, sample size, and complementary information needed to understand the distribution. No single robust statistic can represent every feature of a dataset.

Source checked on 2 November 2026; fictional median deviations independently recalculated.