Median Absolute Deviation Calculator
Calculates the median absolute deviation from the dataset median as a robust scale measure. The page treats median absolute deviation as one statistic, not as a substitute for the sampling design.
Define the data behind median absolute deviation
Median absolute deviation
Descriptive Data conditions that affect median absolute deviation
This page reports the raw MAD, not the normal-consistency-scaled value obtained by multiplying by about 1.4826.
This calculator evaluates a defined arithmetic relationship. Sampling method, dependence, missingness, measurement error, and model fit still determine whether median absolute deviation supports the intended inference.
Dataset and the reported median absolute deviation
Check missing entries, transcription errors, and the measurement scale before calculating median absolute deviation. Values that are codes or category labels should not be treated as numerical measurements merely because they contain digits.
Keep the source order when sequence matters, but recognize that an ordered statistic may sort a copy of the values. Record any exclusions instead of silently deleting an inconvenient observation. For median absolute deviation, that check is tied to the entered dataset.
Checking median absolute deviation from the example
The median is 19.5 and the median of the absolute deviations is 4.5. Repeating one intermediate step by hand provides a check that is independent of the final display.
Change one input by a controlled amount and predict whether median absolute deviation should rise, fall, or remain unchanged. A surprising direction usually signals a unit, denominator, or boundary error.
What median absolute deviation can and cannot support
The calculator answers one descriptive data question. It does not automatically choose the sampling design, confidence method, estimator, or decision threshold for the user. Here, dataset is part of the condition that must remain documented.
Name the parameter or population the result is intended to describe before transferring it to another analysis. For median absolute deviation, that check is tied to the entered dataset.
Units, percentages, and the median absolute deviation denominator
Read the formula without numbers first. Counts, percentages, squared units, and dimensionless ratios should end in a result label consistent with the source measurement scale. On this page, the immediate quantity affected is median absolute deviation.
A scale check can catch a percentage entered as 40 instead of 0.40, or a population count placed where a sample count belongs. The saved median absolute deviation record should make that choice explicit.
Preserving the calculation record
Save median absolute deviation with the source values, sample or population label, calculation convention, and date. Round for the report after dependent calculations are complete.
Do not let the number of displayed digits imply more precision than dataset and dataset can support. This distinction applies directly to the reported median absolute deviation.
How the inputs become median absolute deviation
The printed relationship is MAD = median(|xi - median(x)|). Match every symbol to the labeled fields and carry percentages as proportions when the formula requires them.
Recalculate from the saved dataset if dataset changes. An answer copied without its inputs cannot reproduce the original statistical setup. On this page, the immediate quantity affected is median absolute deviation.
A second credible case for median absolute deviation
Build a second case using values that could occur together, then compare its median absolute deviation with the baseline. This reveals whether the conclusion depends on one uncertain assumption.
When the result changes materially, report both conditions instead of combining the most favorable inputs from separate datasets. For median absolute deviation, that check is tied to the entered dataset.
The same source record may also support dataset percentile, five number summary, dataset quartiles and interquartile range.
The statistical quantity behind median absolute deviation
Calculates the median absolute deviation from the dataset median as a robust scale measure. The reported unit is the dataset’s own unit. The question is defined by the labeled dataset rather than by an assumed population outside the page.
The median is 19.5 and the median of the absolute deviations is 4.5.
Interpreting the displayed median absolute deviation
Does median absolute deviation prove a population conclusion?
No. The calculation supplies a statistic or planning value; sampling design and assumptions govern any inference beyond the entered data. Here, dataset is part of the condition that must remain documented.
Why might another program return a different median absolute deviation?
Different percentile conventions, denominator choices, critical values, missing-data rules, or rounding can produce different answers. That safeguard matters before median absolute deviation is reused elsewhere.
How can the median absolute deviation arithmetic be verified?
Repeat one intermediate step from MAD = median(|xi - median(x)|) and work backward to recover dataset or dataset.
How should median absolute deviation be rounded?
Keep guard digits during checking, then round to the resolution justified by the source values and the decision that follows. Here, dataset is part of the condition that must remain documented.