Description
Return median=lower/2+upper/2 and intervalWidth=upper-lower for ordered supplied middle values.
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.
Return median=lower/2+upper/2 and intervalWidth=upper-lower for ordered supplied middle values.
When to use this tool
Use Sample Median Two Middle Average Range 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 lower, upper. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read median, intervalWidth. Use the output convention below.
Return median=lower/2+upper/2 and intervalWidth=upper-lower for ordered supplied middle values.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| lower | Lower | Required. Finite number. |
| upper | Upper | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| median | Median | Required. Finite number. |
| intervalWidth | Interval Width | Required. Finite number. |
{
"input": {
"lower": 2,
"upper": 8
},
"output": {
"median": 5,
"intervalWidth": 6
}
}Limitations and assumptions
- No sample is provided or sorted, and the middle-value status is assumed. The half-sum reduces addition overflow but does not make every width or extreme-scale operation representable.
- 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
Similar or alternative tools
- Median Tie Middle Gap
Sort a copy of nonempty values numerically and return lowerMiddle, upperMiddle, and gap=upperMiddle-lowerMiddle.
- Arithmetic Geometric Mean Gap Two Values
Return arithmetic=(left+right)/2, geometric=sqrt(left)*sqrt(right), and gap=arithmetic-geometric for nonnegative inputs.