Description
Compute median absolute deviation about an explicitly supplied reference, not automatically the sample median and not normal-consistency scaled.
A descriptive statistic depends on what is counted, how observations are weighted, and which reference or denominator is used. Removing observations differs from replacing them at cutoffs, and a ratio of totals differs from a mean of individual ratios. Keep those conventions and measurement units explicit when comparing results.
Compute median absolute deviation about an explicitly supplied reference, not automatically the sample median and not normal-consistency scaled.
When to use this tool
Use this tool to compute median absolute deviation about an explicitly supplied reference, not automatically the sample median and not normal-consistency scaled.
How to use the tool and how it works
- Enter values, reference using the field definitions below.
- Run the operation. Correct input errors before interpreting an output.
- Read result.deviation. Use the ordering, boundary rules and absence conditions described below.
Compute absolute differences from the supplied reference, sort them and take their median, averaging the two central differences for an even count.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| values | Finite observations in the measurement units used by reference or cutoffs. | Dense list of at most 128 finite numbers; integer/shape constraints above also apply. |
| reference | Caller-supplied center/reference in the observations’ units. | A finite number satisfying the operation’s stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the named fields below. |
| result.deviation | Mean or median absolute distance from the supplied reference, in observation units. |
{
"input": {
"values": [
1,
2,
9
],
"reference": 1
},
"output": {
"result": {
"deviation": 1
}
}
}Limitations and assumptions
- The reference is not estimated and no normal-consistency scaling is applied.
- Use consistent units within each measured list and its reference/cutoffs. Ratios carry numerator units divided by denominator units unless those units cancel. Ordinary floating-point arithmetic is used; input validation does not establish statistical suitability.
- Every declared top-level input field is required and unexpected fields are rejected. Ordinary strings are limited to 8,192 UTF-16 code units and lists to 128 entries, with tighter operation-specific bounds where stated. JSON text has bounded nesting and node counts.
- Numeric outputs must be finite and no larger in absolute magnitude than the safe-integer limit; operations returning exact large integers use decimal text. Positions are zero-based and spans end exclusively unless the operation explicitly states a different convention.
Alternative or Complementary methods
Check the descriptive convention and denominator before comparing results. Use a separate inferential model when you need uncertainty, significance, causal interpretation or population estimates.
References
Similar or alternative tools
- Mean Absolute Deviation from Reference
Compute mean absolute deviation about a caller-supplied reference; existing mean-absolute-deviation centers on the sample mean instead.
- Asymmetric Absolute Deviation Totals
Separate total absolute deviations below and above an explicit reference, retaining asymmetric loss evidence without estimating a distribution.