Mean Absolute Deviation from the Median

Description

Automatically find the sample median and average its absolute deviations, without confusing this mean aggregation with the median absolute deviation statistic.

Mean absolute deviation from the median averages distances from the sample median. It is expressed in the original data units and differs both from median absolute deviation and from deviation about the arithmetic mean.

Automatically find the sample median and average its absolute deviations, without confusing this mean aggregation with the median absolute deviation statistic.

When to use this tool

Use this tool to calculate mean absolute deviation from median under the units, normalization, and boundary conventions below.

How to use the tool and how it works

Supply values in the field shapes below.
Run the calculation. Correct format, shape, range, or undefined-statistic errors before interpreting a result.
Read count, deviation, median. Use the conventions below.

Find the sample median, calculate absolute deviations from it and return their arithmetic mean together with the center and count.^[1]

Input field	Meaning and units	Accepted input
values	Values	Required. Array of Finite number.; minimum items 1; maximum items 512.

Output field	Interpretation	Returned shape
count	Requested count; the mechanics explain whether one draw expands into several returned records.	Required. Safe integer; minimum 1; maximum 512.
deviation	The specified unscaled mean or median absolute deviation, in the same units as values.	Required. Finite number; minimum 0.
median	Sample median in the same units as values.	Required. Finite number.

json

{
  "input": {
    "values": [
      2,
      3,
      3,
      5,
      100
    ]
  },
  "output": {
    "count": 5,
    "deviation": 20,
    "median": 3
  }
}

Limitations and assumptions

This mean aggregation is distinct from median absolute deviation. The output retains the observations’ measurement units and does not imply a distribution, standard-error estimate or outlier threshold.
The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.

Alternative or Complementary methods

Choose the statistic according to the question and data conventions. Inspect the supplied series or matrix and the stated assumptions before comparing outputs from implementations with different defaults.

References

Tool behavior and example: Mean Absolute Deviation from the Median — tool.io

Similar or alternative tools

median absolute deviation
Automatically find the sample median and the unscaled median of its absolute deviations, without a normal-consistency correction.
standard deviation
Calculate the population standard deviation of a finite dataset.