Core capability

engineering.uncertainty.weighted_mean

GUM H.3 inverse-variance weighted mean of independent results of the same measurand: x_w = Σ(x_i/u_i²)/Σ(1/u_i²), u_w = 1/√Σ(1/u_i²). Not combined RSS, not Type A u_A = s/√n, and not GUM propagate. (calculation_version 1.0.0)

Open calculator Evidence Evidence JSON REST API MCP docs Review policy

Trust

Review-policy: engine tested — automated tests, sources, version lock, and evidence published. Supplemental to CVP; not Domain Expert Review. See CVP and Review policy.

Tier: Engine tested — catalog token engine_tested
Calculation version: 1.0.0
Evidence tests: 8/8 calculation tests · golden 0/0 · boundary 5/5 · property 3/3
Engine tested: Yes
Source checked: Yes
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.0 (workspace artifacts agree)

Production attestation: Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (1 capability; 156 remain CURRENT) @ 2026-09-14T03:54:53.650Z
Semantic contract: PASS
Evidence attested at: 2026-09-14T00:43:05.498Z
Last production check: 2026-09-14T00:43:05.498Z
Public / cache: —
Origin: —

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 4/4.

Tool id: weighted-mean
Engine: weighted-mean
REST: POST /api/v1/calc/weighted-mean
MCP: execute_calculation with capability_id: "engineering.uncertainty.weighted_mean"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.0)
Versioned output schema: Immutable pin (1.0.0)

Limitations

Do not use outside this declared scope.

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

Try with an agent

Inspect this capability via same-origin MCP, then call execute_calculation.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"engineering.uncertainty.weighted_mean"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.0.0) when reproducibility matters. Full protocol notes: MCP docs.