Verified calculation capability

Pooled standard deviation Calculation Capability

Pooled s_p = √(Σ ν_i s_i² / Σ ν_i) from k≥2 stated sample standard deviations and their degrees of freedom. Not Type A from one sample, not Welch–Satterthwaite ν_eff, and not ISO 21748 u of a mean. · Engineering · Uncertainty

Capability ID engineering.uncertainty.pooled_sd · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Pooled s

Pooled s: s_p = √(Σ ν_i s_i² / Σ ν_i)
Pooled ν: ν = Σ ν_i

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`s`	Sample standard deviations s_i. Aliases: s_i, stdevs, std. Share-URL: comma-separated.	—	input / output
`nu`	Degrees of freedom ν_i, same length as s. Each ν_i > 0 and finite. Aliases: nu_i, dof, df. If omitted, n_i ≥ 2 gives ν_i = n_i−1.	—	input / output
`n`	Optional sample sizes. Used only when nu is omitted: ν_i = n_i−1.	—	input
`s_p`	Pooled standard deviation √(Σ ν_i s_i² / Σ ν_i)	—	output
`k`	Number of groups	—	output
`nu_i`	—	—	output

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

Assumptions

Pooled standard deviation: s_p = √(Σ ν_i s_i² / Σ ν_i) from k≥2 stated groups. ν_i > 0 and finite.
s_i ≥ 0. Both zero is valid (s_p = 0).
Not Type A from one sample, not Welch–Satterthwaite ν_eff, and not ISO 21748 u of a mean.

Not supported

Type A from one sample
Welch ν_eff
ISO 21748 u of a mean
infinite ν_i
combined RSS

Example

One numerical check. The calculator page holds worked steps and FAQ.

s=[1,7] nu=[1,1] → s_p=5

Open this example in the calculator

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: STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-16T06:44:24.909Z
Semantic contract: PASS
Evidence attested at: 2026-09-16T06:44:24.203Z
Last production check: 2026-09-16T06:44:24.203Z
Public / cache: PASS
Origin: PASS

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: pooled-sd
Engine: pooled-sd
REST: POST /api/v1/calc/pooled-sd
MCP: execute_calculation with capability_id: "engineering.uncertainty.pooled_sd"
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)

References

Human-readable sources plus CVP reference evidence classes.

Sources

JCGM 100:2008 — Evaluation of measurement data (GUM) — 4.2.4 Type A evaluation from several series
ISO 5725-2 — Repeatability and reproducibility of standard measurement methods — Pooled repeatability standard deviation

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.pooled_sd"}}}'

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