Description
Calculate incremental=oldMean+(value-oldMean)/(count+1) and residual=suppliedUpdatedMean-incremental.
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.
Calculate incremental=oldMean+(value-oldMean)/(count+1) and residual=suppliedUpdatedMean-incremental.
When to use this tool
Use Mean Update Finite Precision Residual 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 oldMean, count, value, suppliedUpdatedMean. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read incremental, residual. Use the output convention below.
Calculate incremental=oldMean+(value-oldMean)/(count+1) and residual=suppliedUpdatedMean-incremental. Require nonnegative integer count with room for one additional observation.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| oldMean | Old Mean | Required. Finite number. |
| count | Number of observations before the update, including zero. | Required. Safe integer; minimum 0. |
| value | Value | Required. Finite number. |
| suppliedUpdatedMean | Supplied Updated Mean | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| incremental | Incremental | Required. Finite number. |
| residual | Signed discrepancy under the formula stated above. | Required. Finite number. |
{
"input": {
"oldMean": 4,
"count": 3,
"value": 8,
"suppliedUpdatedMean": 5
},
"output": {
"incremental": 5,
"residual": 0
}
}Limitations and assumptions
- At count zero the old mean still participates in floating-point arithmetic even though it cancels algebraically. This does not verify summaries or guarantee stable arithmetic for extreme values.
- 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
- Arithmetic Geometric Mean Gap Two Values
Return arithmetic=(left+right)/2, geometric=sqrt(left)*sqrt(right), and gap=arithmetic-geometric for nonnegative inputs.
- Arithmetic Harmonic Mean Two Value Gap
Return arithmetic=first/2+second/2, harmonic=2*first*second/(first+second), and gap=arithmetic-harmonic for positive inputs.