Statistics Suite (descriptive stats) mechanism

Model scope

The population variance formula itself is correct under its stated denominator, but the instrument is not fully verifiable because the remaining claimed outputs lack precise definitions. The empty honest_label is a concern: the product should disclose population-versus-sample variance, quartile convention, skewness convention, kurtosis versus excess kurtosis, mode-tie behavior, and box-plot outlier policy before being labeled complete.

• The variance formula σ²=Σ(x-μ)²/n is the population variance formula only; the specification does not state whether sample variance using n-1 is also supported or which one is reported.
• “Standard descriptive-stats formulas” does not define the formulas or conventions for quartiles, skewness, kurtosis, mode ties, or box-plot construction.
• Skewness is ambiguous between moment skewness, adjusted Fisher-Pearson sample skewness, and other definitions.
• Kurtosis is ambiguous between raw kurtosis and excess kurtosis.
• Quartile results depend on the method used for even-sized and small datasets; no quartile convention is specified.
• A box plot requires an explicit five-number-summary and outlier rule, such as Tukey's 1.5×IQR rule, neither of which is specified.

Units and conventions

• Inputs are finite real numbers measured in a common unit.
• Mean, median, mode, quartiles, skewness, and kurtosis are unitless only where mathematically appropriate; variance has squared input units and standard deviation has the original input units.
• The test vectors assume population variance σ²=Σ(x-μ)²/n.
• The test vectors assume median-excluded Tukey quartiles: split an even-sized ordered list into equal halves, and for an odd-sized list exclude the overall median from both halves.
• The test vectors assume moment skewness m3/(m2^(3/2)), where mk=Σ(x-μ)^k/n.
• The test vectors report raw kurtosis m4/(m2²), not excess kurtosis; excess kurtosis is raw kurtosis minus 3.

Inspectable vector

One of 4 source-bound review vectors:

{
  "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]."
}

Failure boundary

• 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.

Other records

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