Median Tie Middle Gap Tool

Description

Sort a copy of nonempty values numerically and return lowerMiddle, upperMiddle, and gap=upperMiddle-lowerMiddle.

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.

Sort a copy of nonempty values numerically and return lowerMiddle, upperMiddle, and gap=upperMiddle-lowerMiddle.

When to use this tool

Use Median Tie Middle Gap 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 values. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read lowerMiddle, upperMiddle, gap. Use the output convention below.

Sort a copy of nonempty values numerically and return lowerMiddle, upperMiddle, and gap=upperMiddle-lowerMiddle.^[1]

Input field	Meaning and units	Accepted input
values	Values	Required. Array of finite number; maximum items 256.

Output field	Interpretation	Returned shape
lowerMiddle	Lower Middle	Required. Finite number.
upperMiddle	Upper Middle	Required. Finite number.
gap	Gap	Required. Finite number.

json

{
  "input": {
    "values": [
      9,
      1,
      5,
      3
    ]
  },
  "output": {
    "lowerMiddle": 3,
    "upperMiddle": 5,
    "gap": 2
  }
}

Limitations and assumptions

For odd length both middle values coincide. The tool does not average them into a returned median, handle missing values, or choose an alternative sample 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/median-tie-middle-gap — tool.io

Similar or alternative tools

Sample Median Two Middle Average Range
Return median=lower/2+upper/2 and intervalWidth=upper-lower for ordered supplied middle values.
Empirical Cdf One Tie Jump
Return leftLimit=less/count, rightLimit=(less+tied)/count, and jump=tied/count after feasible nonnegative integer count checks with positive total.