Mathematics · Statistics

Horvitz–Thompson Weighted Contribution observed sampled-unit value Solver

Rearrange the horvitz–thompson weighted contribution relationship and solve for observed sampled-unit value.

Runs locally
Your numbers

Inputs and results stay in this browser. Change one value at a time to explore the relationship.

Your inputCalculatedPassed forward in chains
observed sampled-unit value18
Reconstructed population-total contribution150

Calculation steps

  1. Use a=cb with population-total contribution=150 and unit inclusion probability=0.12.
  2. observed sampled-unit value=18.
  3. Substitution into c=a/b reconstructs 150.

Understand Horvitz–Thompson Weighted Contribution: solve observed sampled-unit value

One idea, three depths

Choose how deeply to explain Horvitz–Thompson Weighted Contribution: solve observed sampled-unit value

Horvitz–Thompson Weighted Contribution: solve observed sampled-unit value: Rearrange the horvitz–thompson weighted contribution relationship and solve for observed sampled-unit value.

Age 5Explain it to a 5-year-oldStart with a picture

Imagine using Horvitz–Thompson Weighted Contribution: solve observed sampled-unit value to answer this question: rearrange the horvitz–thompson weighted contribution relationship and solve for observed sampled-unit value? Enter population-total contribution and unit inclusion probability; the calculator shows observed sampled-unit value. For example: observed sampled-unit value=18 and unit inclusion probability=0.12 produce population-total contribution=150. The answer tells you observed sampled-unit value.

Age 15Explain it to a 15-year-oldConnect it to the formula

A Horvitz–Thompson contribution divides an observed value by its inclusion probability. This page isolates observed sampled-unit value and verifies it in the original relationship. The rule is a=cb. Its input values are population-total contribution, unit inclusion probability, and the main result is observed sampled-unit value. For example: observed sampled-unit value=18 and unit inclusion probability=0.12 produce population-total contribution=150.

CollegeExplain it at college levelState the model precisely

This calculator evaluates the stated horvitz–thompson weighted contribution: solve observed sampled-unit value relation over the valid real-number domain stated below. The implemented relation is a=cb, evaluated from population-total contribution, unit inclusion probability to produce observed sampled-unit value. A Horvitz–Thompson contribution divides an observed value by its inclusion probability. This page isolates observed sampled-unit value and verifies it in the original relationship. The inclusion probability must be positive and correspond to the actual sampling design.

Inputs and valid domain

  • population-total contribution must be a finite real number.
  • unit inclusion probability must be a finite real number.

Important boundary: The inclusion probability must be positive and correspond to the actual sampling design.

The formula

a=cb

How the calculator works through it

It substitutes population-total contribution, unit inclusion probability into the formula and exposes every numerical step above. The main output is observed sampled-unit value, accompanied by Reconstructed population-total contribution.

Read the result correctly

The observed sampled-unit value is the direct answer to “rearrange the horvitz–thompson weighted contribution relationship and solve for observed sampled-unit value.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.

A worked check

observed sampled-unit value=18 and unit inclusion probability=0.12 produce population-total contribution=150.

Where this model stops being reliable

The inclusion probability must be positive and correspond to the actual sampling design.

Learn it by changing one value

Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.

Dictionary terms behind this calculator

Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.

These foundations help you understand why Horvitz–Thompson Weighted Contribution: solve observed sampled-unit value works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.

Hard requirements

  • Reading formulas and substituting values

    Horvitz–Thompson Weighted Contribution: solve observed sampled-unit value uses a=cb. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.

    Review this foundation about 4 min

Strong support

  • Averages and representative values

    Representative values help you judge what the Horvitz–Thompson Weighted Contribution: solve observed sampled-unit value inputs summarise and what the result can legitimately describe.

    Review this foundation about 5 min

Optional enrichment

  • Spread and measurement variation

    Variation is not always part of the Horvitz–Thompson Weighted Contribution: solve observed sampled-unit value formula, but it helps you judge how stable a reported result may be.

    Review this foundation about 6 min
Learn the missing foundationsI already know these — show the code

Mathematics → algorithm → program

Implement this calculation in code

These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.

Algorithm

  1. Read population-total contribution, unit inclusion probability.
  2. Evaluate the principal relationship: a=cb.
  3. Return observed sampled-unit value and check the domain conditions described above.
Python
            from math import *

def horvitz_thompson_contribution_solve_a(c, b) -> float:
    return (c * b)

assert abs(horvitz_thompson_contribution_solve_a(150, 0.12) - 18) < 1e-6 * max(1.0, abs(18))
          
Current calculator valuesUpdates when you change an input above.
              
            
C
            #include <assert.h>
#include <math.h>

double horvitz_thompson_contribution_solve_a(double c, double b) {
    return (c * b);
}

int main(void) {
    const double expected = 18;
    const double actual = horvitz_thompson_contribution_solve_a(150, 0.12);
    assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
C++
            #include <cassert>
#include <cmath>
#include <numbers>

double horvitz_thompson_contribution_solve_a(double c, double b) {
    return (c * b);
}

int main() {
    constexpr double expected = 18;
    const double actual = horvitz_thompson_contribution_solve_a(150, 0.12);
    assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
Linux x86-64 assembly

x86-64 NASM · System V ABI · Linux · SSE2 with libm where required

            ; double horvitz_thompson_contribution_solve_a(double c, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global horvitz_thompson_contribution_solve_a
section .text

horvitz_thompson_contribution_solve_a:
    push rbp
    mov rbp, rsp
    sub rsp, 32
    movsd [rbp-8], xmm0
    movsd [rbp-16], xmm1
    movsd xmm0, [rbp-8]
    mulsd xmm0, [rbp-16]
    movsd [rbp-24], xmm0
    movsd xmm0, [rbp-24]
    leave
    ret
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = horvitz_thompson_contribution_solve_a(c, b)
    result = (c * b);
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[c_, b_] := (c * b);
          
Current calculator valuesUpdates when you change an input above.
              
            

Continue in mathematical software

The downloaded file includes your current inputs and first calculated result. It is created locally.

Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.

Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations

Standards, reading and academic references

Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.

Introductory Statistics 2e

Read the free OpenStax statistics textbook
Cite this book
APA 7
Illowsky, B., & Dean, S. (2023). Introductory statistics 2e. OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction
MLA 9
Illowsky, Barbara, and Susan Dean. Introductory Statistics 2e. OpenStax, 2023, https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
Chicago author-date
Illowsky, Barbara, and Susan Dean. 2023. Introductory Statistics 2e. Houston, TX: OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.

OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.

Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS

These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.

APA 7

MW SysArc. (2026, July 21). Horvitz–Thompson Weighted Contribution observed sampled-unit value Solver. MW SysArc Tools. https://math.mwsysarc.com/statistics/horvitz-thompson-contribution-observed-sampled-unit-value-solver

MLA 9

MW SysArc. “Horvitz–Thompson Weighted Contribution observed sampled-unit value Solver.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/statistics/horvitz-thompson-contribution-observed-sampled-unit-value-solver. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “Horvitz–Thompson Weighted Contribution observed sampled-unit value Solver.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/statistics/horvitz-thompson-contribution-observed-sampled-unit-value-solver.

Harvard

MW SysArc (2026) ‘Horvitz–Thompson Weighted Contribution observed sampled-unit value Solver’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/statistics/horvitz-thompson-contribution-observed-sampled-unit-value-solver (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_horvitz_thompson_contribution_solve_a_2026,
  author = {{MW SysArc}},
  title = {Horvitz–Thompson Weighted Contribution observed sampled-unit value Solver},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/statistics/horvitz-thompson-contribution-observed-sampled-unit-value-solver},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - Horvitz–Thompson Weighted Contribution observed sampled-unit value Solver
T2  - MW SysArc Tools
PY  - 2026
DA  - 2026-07-21
Y2  - 2026-08-31
UR  - https://math.mwsysarc.com/statistics/horvitz-thompson-contribution-observed-sampled-unit-value-solver
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the Horvitz–Thompson Weighted Contribution: solve observed sampled-unit value do?

Rearrange the horvitz–thompson weighted contribution relationship and solve for observed sampled-unit value.

How does the Horvitz–Thompson Weighted Contribution: solve observed sampled-unit value work?

The calculator applies a=cb. A Horvitz–Thompson contribution divides an observed value by its inclusion probability. This page isolates observed sampled-unit value and verifies it in the original relationship.

What can I learn from the Horvitz–Thompson Weighted Contribution: solve observed sampled-unit value?

It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.

Does MW SysArc receive or store what I enter?

No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.

How should I use the result?

Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.

Last reviewed . Calculations tested .

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