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Coefficient of Variation and Scale Comparability

Install and import#

bash
npm install fintech-algorithms
ts
import { coefficientOfVariationAndScaleComparability } from "fintech-algorithms/foundations/dispersion-shape-and-robust-statistics/coefficient-of-variation-and-scale-comparability";

Signature#

coefficientOfVariationAndScaleComparability(input)

Divides the sample standard deviation by the absolute value of the mean, turning spread into a unit-free figure that can be compared across series measured on different scales.

Parameters#

NameTypeNotes
input{ values: number[] }The observations to measure, under the key values. The ratio is only meaningful for series on a ratio scale with a mean away from zero.
values: at least two observations, and a non-zero mean

Returns#

{ coefficientOfVariation: number; scaleFree: boolean }

coefficientOfVariation is the sample standard deviation over the absolute mean, and scaleFree is always true, marking the figure as carrying no units.

Errors#

  • When input is null, an array, or not an object — throws TypeError
  • When values is missing, is not an array, or is empty — throws RangeError
  • When any entry of values does not coerce to a finite number — throws RangeError
  • When values holds fewer than two observations, so the sample divisor n - 1 would be zero — throws RangeError
  • When the arithmetic mean of values is exactly zero, leaving the ratio undefined — throws RangeError

Complexity: time O(n log n), space O(n).

Worked example#

verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

Input#

input
{
  "values": [1, 2, 2, 4, 9]
}

Call#

coefficientOfVariationAndScaleComparability(input)

Returns#

object with 2 fields: coefficientOfVariation, scaleFree

{
  "coefficientOfVariation": 0.8914892519934007,
  "scaleFree": true
}

Diagrams#

Coefficient of Variation and Scale Comparability — article hero
Coefficient of Variation and Scale Comparability — calculation ledger
Coefficient of Variation and Scale Comparability — concept anatomy
Coefficient of Variation and Scale Comparability — failure boundary
Coefficient of Variation and Scale Comparability — method map
Coefficient of Variation and Scale Comparability — scenario contrast

Calculation flow#

Reasoning flow — D00-F05-A07 
flowchart LR
    A["Synthetic input + metadata"] --> B{"Contract valid?"}
    B -->|No| C["Reject or route with reason"]
    B -->|Yes| D["Apply Coefficient of Variation and Scale Comparability"]
    D --> E["Formula: CV=s/|x̄|"]
    E --> F["Verified fixture output"]
    F --> G{"Interpretation within boundary?"}
    G -->|Yes| H["Report value + convention + audit"]
    G -->|No| I["Add companion view or narrower claim"]

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

The rest of the Dispersion, Shape, and Robust Statistics family#