engineering.uncertainty.weighted_mean

Three distinct suites: educational examples on the calculator page, this legacy regression count (9/9 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.0.1 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-09-23.o2-o3. Calculation version 1.0.1. CVP 1.0.0-proposed. 5/5 golden · 5/5 CVP boundary · 7/7 invalid · 2/2 property · 2/2 metamorphic · 8/8 O3 · 4/4 cross-interface · 6/6 CVP contract. digest 77bc67046423. O2: JCGM 100 H.3 inverse-variance weighted mean vs separate-module identities (≤2 ULP). Not RSS, not Type A, and not U=k·u_w. ≤2 ULP vs O3 applies only to the published tabulated H.3 vectors (equal weights, unequal weights, a single result, aliases, a signed measurand, doubled uncertainties, and one awkward triple). It is not a whole-domain guarantee and does not cover RSS, Type A, or U=k·u_w.

• Golden (oracle-backed) 5 / 5
• CVP boundary 5 / 5
• Invalid input 7 / 7
• Property 2 / 2
• Metamorphic 2 / 2
• O3 high-precision 8 / 8
• Cross-interface 4 / 4
• CVP contract 6 / 6
• Interfaces PASS · UI (SSR) / REST / MCP
• Interface claim ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
• Verified scope JCGM 100 H.3 x_w = Σ(x_i/u_i²)/Σ(1/u_i²) and u_w = 1/√Σ(1/u_i²), plus χ² and Birge diagnostics, + O3 mpmath tabulated x_w.
• Assurance Engineering
• Deferred Not combined RSS, not Type A u_A = s/√n, and not expanded U = k·u_w.

• release artifacts aligned PASS
• schema output required declared PASS
• schema valid input executes PASS
• engine success output validates schema PASS
• schema rejects incomplete input PASS
• rest success payload validates schema PASS

Fingerprint sha256:fba713ade5bb42da5de3ab874d710f916eb663100287fb35102725987ee0740d

Input schema sha256:da008f579c37f7c7c08cd298509b622dfe4ee81c41ed32349e926b804c153c47 · Output schema sha256:d2629b5ce5875b7414b46d84e47b0e0793e4e7c060d9f4e49b8747c6cd45997d · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Tool

weighted-mean

Engine

weighted-mean

Engine build

2026-09-23

Evidence core

2026-09-23T09:08:38.031Z

Rendered

2026-10-22T08:54:34.768Z

Last reviewed

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Assumptions

• JCGM 100:2008 H.3 inverse-variance weighted mean of independent uncorrelated results of the same measurand
• Each u_i is a standard uncertainty greater than zero
• Not combined RSS, not Type A u_A = s/√n, and not GUM propagate
• χ² / Birge are diagnostics, not a pass/fail

Limitations

• Independent uncorrelated results of the same measurand — not RSS of a measurement model
• Does not compute Type A u_A = s/√n from repeats without individual u_i
• Does not compute expanded U = k·u_w
• χ² / Birge are diagnostics, not a pass/fail verdict