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Population and Sample Standard Deviation

Install and import#

bash
npm install fintech-algorithms
ts
import { populationAndSampleStandardDeviation } from "fintech-algorithms/foundations/dispersion-shape-and-robust-statistics/population-and-sample-standard-deviation";

Signature#

populationAndSampleStandardDeviation(input)

Takes the square root of both the population and the sample variance of one series, returning spread in the same units as the observations.

Parameters#

NameTypeNotes
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

Returns#

{ populationStandardDeviation: number; sampleStandardDeviation: number }

The square roots of the n-divisor and n - 1-divisor variances respectively.

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

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#

populationAndSampleStandardDeviation(input)

Returns#

object with 2 fields: populationStandardDeviation, sampleStandardDeviation

{
  "populationStandardDeviation": 2.870540018881465,
  "sampleStandardDeviation": 3.2093613071762426
}

Diagrams#

Population and Sample Standard Deviation — article hero
Population and Sample Standard Deviation — calculation ledger
Population and Sample Standard Deviation — concept anatomy
Population and Sample Standard Deviation — failure boundary
Population and Sample Standard Deviation — method map
Population and Sample Standard Deviation — scenario contrast

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#