Source: https://guthlabs.ai/docs/instruments/statistics-suite-descriptive-stats/implementation/

instrument implementation / implementation-contract

# Statistics Suite (descriptive stats) implementation

A source-bound implementation contract for Statistics Suite (descriptive stats); deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t4-213

**Effect**: Computation or source lookup only

## Input and validation requirements

- Empty data lists make mean, median, variance, standard deviation, quartiles, skewness, kurtosis, and the box plot undefined.

- Skewness divides by m2^(3/2) and kurtosis divides by m2²; constant data cause division by zero.

- Sample variance divides by n-1 and is undefined for a one-observation dataset; the specification does not state whether sample variance is supported.

- Mode can be non-unique or absent; the output policy for ties and no mode is unspecified.

- Quartiles for datasets with fewer than two or three observations require an explicit policy.

- Non-numeric, non-finite, or mixed-unit inputs require validation and rejection.

- Box-plot outlier whiskers and plotted points depend on an unspecified outlier rule.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "data": [
      1,
      2,
      3,
      4,
      5
    ]
  },
  "expected_outputs": {
    "mean": 3,
    "median": 3,
    "mode": null,
    "variance": 2,
    "standard_deviation": 1.4142135624,
    "q1": 1.5,
    "q3": 4.5,
    "skewness": 0,
    "kurtosis": 1.7,
    "box_plot": {
      "minimum": 1,
      "q1": 1.5,
      "median": 3,
      "q3": 4.5,
      "maximum": 5
    }
  },
  "working": "μ=(1+2+3+4+5)/5=15/5=3.\nDeviations are -2,-1,0,1,2; squared deviations sum to 4+1+0+1+4=10.\nVariance=10/5=2; standard deviation=√2=1.4142135624.\nMedian=3; every value occurs once, so there is no mode.\nLower half [1,2] gives Q1=(1+2)/2=1.5; upper half [4,5] gives Q3=(4+5)/2=4.5.\nThe third-power deviations sum to -8-1+0+1+8=0, so skewness=0/2^(3/2)=0.\nFourth-power deviations sum to 16+1+0+1+16=34; m4=34/5=6.8; kurtosis=6.8/(2²)=6.8/4=1.7.\nFive-number summary=[1,1.5,3,4.5,5]."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/statistics-suite-descriptive-stats/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/statistics-suite-descriptive-stats/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/statistics-suite-descriptive-stats/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche4/tranche4-results.json`