Median Absolute Deviation
Install and import#
npm install fintech-algorithmsimport { medianAbsoluteDeviation } from "fintech-algorithms/foundations/dispersion-shape-and-robust-statistics/median-absolute-deviation";Signature#
medianAbsoluteDeviation(input)Takes the median of the absolute distances from the series median, and rescales it by 1.4826 so it lines up with a standard deviation under normality.
Parameters#
| Name | Type | Notes |
|---|---|---|
input | { values: number[] } | The observations to measure, under the key values. Both the centre and the spread are medians, so a handful of extreme observations cannot drag the result. |
Returns#
{ medianAbsoluteDeviation: number; median: number; scaledMad: number }
medianAbsoluteDeviation is the raw median of the absolute deviations, median is the centre they were taken from, and scaledMad is that raw figure multiplied by 1.4826.
Errors#
- When
inputis null, an array, or not an object — throws TypeError - When
valuesis missing, is not an array, or is empty — throws RangeError - When any entry of
valuesdoes not coerce to a finite number — throws RangeError
Complexity: time O(n log n),
space O(n).
Worked example#
verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.
Input#
{
"values": [1, 2, 2, 4, 9]
}Call#
medianAbsoluteDeviation(input)Returns#
object with 2 fields: medianAbsoluteDeviation, median
{
"medianAbsoluteDeviation": 1,
"median": 2
}Diagrams#
How it works#
This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.
References#
- Measures of Scale — NIST/SEMATECH e-Handbook
- Skewness and Kurtosis — NIST/SEMATECH e-Handbook
- Historical-example decision