Population and Sample Variance

Install and import#

bash

npm install fintech-algorithms

import { populationAndSampleVariance } from "fintech-algorithms/foundations/dispersion-shape-and-robust-statistics/population-and-sample-variance";

populationAndSampleVariance(input)

Averages the squared deviations from the mean twice over the same series: once dividing by the observation count, once by that count less one.

Name	Type	Notes
`input`	`{ values: number[] }`	The observations to measure, under the key `values`. At least two are needed, because the sample figure divides by `n - 1`. values: at least two observations

{ populationVariance: number; sampleVariance: number }

populationVariance divides the sum of squared deviations by n, sampleVariance divides it by n - 1.

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

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

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

input

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

populationAndSampleVariance(input)

object with 2 fields: populationVariance, sampleVariance

{
  "populationVariance": 8.24,
  "sampleVariance": 10.3
}

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