Description
Remove a supplied contribution using remainingMean=(mean*totalWeight-value*weight)/(totalWeight-weight).
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.
Remove a supplied contribution using remainingMean=(mean*totalWeight-value*weight)/(totalWeight-weight).
When to use this tool
Use Weighted Mean One Observation Deletion Term 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 mean, totalWeight, value, weight. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read remainingMean. Use the output convention below.
Remove a supplied contribution using remainingMean=(mean*totalWeight-value*weight)/(totalWeight-weight). Require positive total weight and removed weight from zero inclusive to total exclusive.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| mean | Mean | Required. Finite number. |
| totalWeight | Total Weight | Required. Finite number; strictly above 0. |
| value | Value | Required. Finite number. |
| weight | Supplied weight; interpretation follows the stated model rather than an inferred probability. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| remainingMean | Remaining Mean | Required. Finite number. |
{
"input": {
"mean": 5,
"totalWeight": 10,
"value": 8,
"weight": 2
},
"output": {
"remainingMean": 4.25
}
}Limitations and assumptions
- The summaries must describe the same weighted dataset. This does not locate an observation, verify its original weight, recompute uncertainty, or diagnose an influential data point.
- 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
- Geometric Mean Log Deletion Term
Subtract log(removedValue) from logSum, divide by count-1 for logMean, and exponentiate for remainingGeometricMean.
- Weighted Mean Centering Term
Return weightedResidual=weight*(value-center), requiring nonnegative weight.