Can a variance calculation preserve a small spread?

What will you examine?

The five integers are 999999998, 999999999, 1000000000, 1000000001 and 1000000002.

Compare raw second moments, Welford's recurrence, statistics.pvariance and an exact rational reference.

What does the question assume?

Population variance divides by five; sample variance divides by four and is a different target.

The five stated integers are exactly representable as binary floats; intermediates can still round.

What should you compare?

The exact mean is 1000000000 and centered squared offsets sum to 10, giving population variance 2.

Retain all inputs and every method's output, including a poor numerical result. Do not treat agreement with the author's own reference as independent verification.

An optional, separately requested finite-statistic predicate checks only the exact variance of these five decimal constants. It does not check any variance implementation.

What could the evidence establish?

Five values establish no universal method ranking, floating-point error bound or measurement authenticity.

Other offsets, scales, input orders, extreme values and real datasets require new explicit inputs and evidence.

The template begins without a receipt; the optional predicate cannot certify the comparison claim or its prose.

Prepare, then authorize the work.

1. Review the question, inputs, comparison and limits; the template has no scientific result.

2. Prepare an editable draft, supply your own byline, title and scoped claims, and review them before saving privately.

3. Obtain source you may use, or implement the question yourself; select one case and attach your own paper.md in the source ZIP. Do not run submitted code on your host.

4. Upload opaque source bytes through your project. Record the actual archive SHA-256; an inspection of the staged file hashes is not an ingestion result.

5. Review and accept the current bounded ingestion quote. Only qualified isolated ingestion can resolve the source inventory for this exact version.

6. Then review and accept a separate quote for the one author job. Inspect the selected case's status and output, including missing or failed results; an exit code is insufficient.

7. Any independent predicate, model review, contribution or sharing is a separate request with its own scope, permissions and budget.

Bring source you may use.

The inspected original source remains local staging material. Its MIT/CC BY/CC0 terms are proposed, not a released license grant. Obtain permitted source or supply your own implementation. The source-version digest is not an archive digest.

Archive download unavailable. The source remains local staging material with proposed, unreleased license terms.