Ordinal Median Class Boundary Tool

Description

Select a weighted ordinal median under an equality policy.

Ordinal labels have an order, but adjacent categories need not be equally spaced measurements. Index distances, cumulative targets and weighted medians preserve a specified ordering while probability normalization, equality at a median boundary and distance costs remain distinct conventions.

Select a weighted ordinal median under an equality policy.

When to use this tool

Use Ordinal Median Class Boundary when evaluating the stated ordered-label target, distance or mass convention.

How to use the tool and how it works

Enter orderedClasses, probabilities, equalityToLower. Follow any array-alignment requirements below. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read classIndex, classLabel, cumulativeMass. Use the output convention below.

Select a weighted ordinal median under an equality policy. Require aligned unique orderedClasses/nonnegative weights with positive total; choose first cumulative mass >= half when equalityToLower, otherwise > half; return index, label and raw cumulativeMass.^[1]

Input field	Meaning and units	Accepted input
orderedClasses	Ordered Classes	Required. Array of text; maximum UTF-16 length 8192; maximum items 256.
probabilities	Nonnegative ordinal weights with positive sum; normalization to one is not required.	Required. Array of finite number; minimum 0; maximum items 256.
equalityToLower	Equality To Lower	Required. Boolean.

Output field	Interpretation	Returned shape
classIndex	Class Index	Required. Safe integer.
classLabel	Class Label	Required. Text; maximum UTF-16 length 8192.
cumulativeMass	Raw cumulative weight through the selected class, not a normalized probability.	Required. Finite number.

json

{
  "input": {
    "orderedClasses": [
      "A",
      "B",
      "C"
    ],
    "probabilities": [
      0.5,
      0.25,
      0.25
    ],
    "equalityToLower": true
  },
  "output": {
    "classIndex": 0,
    "classLabel": "A",
    "cumulativeMass": 0.5
  }
}

Limitations and assumptions

Weights need not sum to one; the input order defines ordinality and no median confidence or calibrated probabilities are inferred.
Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.

Alternative or Complementary methods

Use meaningful ordered labels and an appropriate ordinal model; evaluate prediction quality with costs and probability assumptions justified for the actual categories.

References

Calculation and input contract: classification/ordinal-median-class-boundary — tool.io

Similar or alternative tools

Ordinal Probability Mass Interval
Return probability mass over a closed ordinal-index interval.
Ordinal Label Cost Matrix Cell
Return ordinal class error cost.