Median Absolute Deviation Calculator
Calculates the median absolute deviation from the dataset median as a robust scale measure. The form displays MAD = median(|xi - median(x)|) beside median absolute deviation, using a worked condition that can be recalculated with the labeled inputs.
Define the data behind median absolute deviation
Median absolute deviation
The question behind median absolute deviation
The median absolute deviation page calculates the median absolute deviation from the dataset median as a robust scale measure.
Median absolute deviation is limited to the statistical quantity named by the result panel. The median absolute deviation calculation does not silently add a population, time horizon, causal direction, or decision threshold that is absent from the fields.
A nearby method may answer the next question: dataset percentile, five number summary, dataset quartiles, and interquartile range.
Reading the median absolute deviation fields
- Dataset: For median absolute deviation, the displayed dataset sequence is 12, 15, 18, 18, 21, 24, 27, 30. Preserve dataset order when median absolute deviation depends on pairing, lag, rank, or time position, and distinguish an observed zero from a missing dataset entry.
The entries used for median absolute deviation must refer to one coherent analysis condition. Combining incompatible populations, periods, or measurement definitions can produce valid median absolute deviation arithmetic for a nonexistent study.
The arithmetic used for median absolute deviation
For median absolute deviation, match every symbol in the relationship to a labeled field before substituting numbers. Median absolute deviation is reported in the scale implied by the inputs and formula.
While checking median absolute deviation, use dataset observations from one defined analysis set rather than totals copied from incompatible groups.
Verifying the default median absolute deviation result
The default median absolute deviation condition is Dataset = 12, 15, 18, 18, 21, 24, 27, 30.
The median is 19.5 and the median of the absolute deviations is 4.5.
The live calculator reports Median absolute deviation 4.5 · Median 19.5. Repeating one intermediate step from MAD = median(|xi - median(x)|) provides a fixed median absolute deviation reference check for later code changes.
Assumptions behind median absolute deviation
This page reports the raw MAD, not the normal-consistency-scaled value obtained by multiplying by about 1.4826.
For median absolute deviation, the result summarizes the observations supplied to this page; extending it to a wider population requires a sampling argument that the arithmetic cannot provide.
A second check on median absolute deviation
When interpreting median absolute deviation, check the observation definition, missing-value treatment, and measurement scale before treating a descriptive statistic as comparable across datasets.
As a second check for median absolute deviation, outliers, ties, ordering, and missing entries can affect median absolute deviation even when the number of observations stays unchanged.
Common failure modes for median absolute deviation
Before accepting median absolute deviation, compare every entered value with its label, unit, and allowed domain after reading the printed relationship from left to right.
For median absolute deviation, do not substitute zero for an unobserved value; missingness and a measured zero describe different data.
Another median absolute deviation failure occurs when a rounded output is reused as though it were the original measurement. Carry guard digits through calculations that depend on median absolute deviation, then round only the reported value.
A reproducible record of median absolute deviation
Report median absolute deviation using MAD = median(|xi - median(x)|), followed by the entered values, units, exclusions, and analysis date. Name the median absolute deviation population or dataset boundary instead of leaving it implicit.
Keep the full calculator output with the record, including Median absolute deviation 4.5 · Median 19.5. A later median absolute deviation review can then distinguish a changed input from a different convention or software implementation.
Questions about median absolute deviation
Does median absolute deviation establish a causal or population conclusion?
No. The displayed median absolute deviation value is conditional on the entered data and named method. The median absolute deviation design, measurement process, and assumptions determine what can be concluded beyond those values.
How should median absolute deviation be rounded?
Keep the unrounded median absolute deviation for subsequent arithmetic, then report only the precision supported by the source measurements and the decision context. Extra digits in median absolute deviation do not correct sampling or model error.