Quartile Rule Midpoint Index Tool

Description

Half-sample membership indices for median-of-halves quartiles, with explicit odd-median inclusion.

A statistical term depends on its data summaries, weighting convention, centering, denominator, and boundary rules. A contribution, derivative, domain check, or converted summary answers a narrower question than a complete estimator. Those conventions must match before terms are combined or compared.

Half-sample membership indices for median-of-halves quartiles, with explicit odd-median inclusion.

When to use this tool

Use Quartile Rule Midpoint Index when you need this specific summary conversion, contribution, domain rule, or sensitivity term with matching statistical conventions.

How to use the tool and how it works

Enter count, quartile, includeMedian. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read lowerHalfCount, upperHalfStart. Use the output convention below.

For count at least two and quartile one or three, return lowerHalfCount and the chosen half's zero-based start, including the central observation in both halves only when includeMedian and count is odd.^[1]

Input field	Meaning and units	Accepted input
count	Count under the stated input or output convention.	Required. Safe integer; minimum 2.
quartile	Quartile	Required. Safe integer.
includeMedian	Include Median	Required. Boolean.

Output field	Interpretation	Returned shape
lowerHalfCount	Lower Half Count	Required. Safe integer.
upperHalfStart	Start of the selected half; zero for first-quartile requests despite the field name.	Required. Safe integer.

json

{
  "input": {
    "count": 9,
    "quartile": 3,
    "includeMedian": false
  },
  "output": {
    "lowerHalfCount": 4,
    "upperHalfStart": 5
  }
}

Limitations and assumptions

The output field upperHalfStart is zero for a first-quartile request. These are half-selection indices, not quartile values or a universal quantile convention.
The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
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. Signed zero is exported as zero.

Alternative or Complementary methods

Use a complete estimator or model when a contribution, sensitivity, or domain check is insufficient. Verify the weight semantics, centering, denominator, and sampling assumptions before combining summaries.

References

Calculation and input contract: statistics/quartile-rule-midpoint-index — tool.io

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