Description
Update count to count+1, mean by (value-mean)/(count+1), and m2 by the product of the old-mean and new-mean deviations.
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.
Update count to count+1, mean by (value-mean)/(count+1), and m2 by the product of the old-mean and new-mean deviations.
When to use this tool
Use Centered Sum Observation Update 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, value. 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. Use the output convention below.
Update count to count+1, mean by (value-mean)/(count+1), and m2 by the product of the old-mean and new-mean deviations. Require positive integer count and nonnegative original m2.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| count | Count under the stated input or output convention. | Required. Safe integer; minimum 1. |
| mean | Mean | Required. Finite number. |
| m2 | M2 | Required. Finite number. |
| value | Value | 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 | M2 | Required. Finite number. |
{
"input": {
"count": 2,
"mean": 3,
"m2": 2,
"value": 6
},
"output": {
"count": 3,
"mean": 4,
"m2": 8
}
}Limitations and assumptions
- M2 is the sum of squared deviations, not variance itself. The summaries must refer to one dataset, and output range checks still apply near numeric or integer limits.
- 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
- Empirical Cdf Single Observation Step
Return one/sampleSize when observation is below evaluation under strict or below-or-equal otherwise, and zero when it fails.
- Mean Update Finite Precision Residual
Calculate incremental=oldMean+(value-oldMean)/(count+1) and residual=suppliedUpdatedMean-incremental.