Description
Remove one observation from count, mean, and centered sum m2, update the mean, and subtract its centered contribution.
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 one observation from count, mean, and centered sum m2, update the mean, and subtract its centered contribution.
When to use this tool
Use Sample Variance One Point 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 count, mean, m2, removed. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read count, mean, m2, variance. Use the output convention below.
Remove one observation from count, mean, and centered sum m2, update the mean, and subtract its centered contribution. Require count at least three, m2 nonnegative, and updated m2>=-1e-10; clamp a permitted negative remainder to zero and return sample variance.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| count | Count under the stated input or output convention. | Required. Safe integer; minimum 3. |
| mean | Mean | Required. Finite number. |
| m2 | Centered sum of squared deviations, not variance. | Required. Finite number. |
| removed | Removed | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| count | Count under the stated input or output convention. | Required. Safe integer. |
| mean | Mean | Required. Finite number. |
| m2 | Centered sum of squared deviations, not variance. | Required. Finite number. |
| variance | Variance | Required. Finite number. |
{
"input": {
"count": 3,
"mean": 4,
"m2": 8,
"removed": 6
},
"output": {
"count": 2,
"mean": 3,
"m2": 2,
"variance": 2
}
}Limitations and assumptions
- The summaries must describe a real common dataset. The fixed 1e-10 tolerance is absolute in squared-data units, not relative error or a statistical decision rule.
- 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
- Sample Variance Denominator Residual
Calculate denominator=sampleCount-correction, expectedVariance=sumSquaredDeviations/denominator, and residual=reportedVariance-expectedVariance.
- Effective Sample Size Weight Split
Split oldWeight into firstPart and its remainder, replace its squared contribution in sumSquaredWeights, and compare effective sizes sumWeights²/squaredSum before and after.