Mathematics · Statistics
Weighted Mean Calculator
Calculate the weighted mean of three values when observations have different importance or frequency.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Weighted sum = 70×1 + 80×2 + 90×1 = 320.
- Sum of weights = 4.
- Weighted mean = 320 ÷ 4 = 80.
Understand Weighted mean
One idea, three depths
Choose how deeply to explain Weighted mean
Calculate the weighted mean of three values when observations have different importance or frequency.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Weighted mean to answer this question: calculate the weighted mean of three values when observations have different importance or frequency? Enter Value 1, Weight 1, Value 2, and 3 other inputs; the calculator shows Weighted mean. For example: Values 70, 80 and 90 with weights 1, 2 and 1 have weighted mean 80. The answer tells you Weighted mean.
Age 15Explain it to a 15-year-oldConnect it to the formula
Each value contributes in proportion to its weight, so larger weights exert more influence on the mean. The rule is Weighted mean = Σ(wx) ÷ Σw. Its input values are Value 1, Weight 1, Value 2, Weight 2, Value 3, Weight 3, and the main result is Weighted mean. For example: Values 70, 80 and 90 with weights 1, 2 and 1 have weighted mean 80.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated weighted mean relation over the valid real-number domain stated below. The implemented relation is Weighted mean = Σ(wx) ÷ Σw, evaluated from Value 1, Weight 1, Value 2, Weight 2, Value 3, Weight 3 to produce Weighted mean. Each value contributes in proportion to its weight, so larger weights exert more influence on the mean. Divide by the sum of weights, not by the number of entered values.
Inputs and valid domain
- Value 1 must be a finite real number.
- Weight 1 must be a finite real number, at least 0.
- Value 2 must be a finite real number.
- Weight 2 must be a finite real number, at least 0.
- Value 3 must be a finite real number.
- Weight 3 must be a finite real number, at least 0.
Important boundary: Divide by the sum of weights, not by the number of entered values.
The formula
Weighted mean = Σ(wx) ÷ Σw
How the calculator works through it
It substitutes Value 1, Weight 1, Value 2, Weight 2, Value 3, Weight 3 into the formula and exposes every numerical step above. The main output is Weighted mean, accompanied by Sum of weights, Weighted sum.
Read the result correctly
The Weighted mean is the direct answer to “calculate the weighted mean of three values when observations have different importance or frequency.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
Values 70, 80 and 90 with weights 1, 2 and 1 have weighted mean 80.
Where this model stops being reliable
Divide by the sum of weights, not by the number of entered values.
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 Weighted mean works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Weighted mean uses Weighted mean = Σ(wx) ÷ Σw. 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 Weighted mean 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 Weighted mean formula, but it helps you judge how stable a reported result may be.
Review this foundation about 6 min
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
- Read Value 1, Weight 1, Value 2, Weight 2, Value 3, Weight 3.
- Evaluate the principal relationship: Weighted mean = Σ(wx) ÷ Σw.
- Return Weighted mean and check the domain conditions described above.
Python
from math import *
def weighted_mean(v1, a, v2, b, v3, c) -> float:
return ((((v1 * a) + (v2 * b)) + (v3 * c)) / ((a + b) + c))
assert abs(weighted_mean(70, 1, 80, 2, 90, 1) - 80) < 1e-6 * max(1.0, abs(80))
C
#include <assert.h>
#include <math.h>
double weighted_mean(double v1, double a, double v2, double b, double v3, double c) {
return ((((v1 * a) + (v2 * b)) + (v3 * c)) / ((a + b) + c));
}
int main(void) {
const double expected = 80;
const double actual = weighted_mean(70, 1, 80, 2, 90, 1);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double weighted_mean(double v1, double a, double v2, double b, double v3, double c) {
return ((((v1 * a) + (v2 * b)) + (v3 * c)) / ((a + b) + c));
}
int main() {
constexpr double expected = 80;
const double actual = weighted_mean(70, 1, 80, 2, 90, 1);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double weighted_mean(double v1, double a, double v2, double b, double v3, double c)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global weighted_mean
section .text
weighted_mean:
push rbp
mov rbp, rsp
sub rsp, 112
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd [rbp-24], xmm2
movsd [rbp-32], xmm3
movsd [rbp-40], xmm4
movsd [rbp-48], xmm5
movsd xmm0, [rbp-8]
mulsd xmm0, [rbp-16]
movsd [rbp-80], xmm0
movsd xmm0, [rbp-24]
mulsd xmm0, [rbp-32]
movsd [rbp-88], xmm0
movsd xmm0, [rbp-80]
addsd xmm0, [rbp-88]
movsd [rbp-72], xmm0
movsd xmm0, [rbp-40]
mulsd xmm0, [rbp-48]
movsd [rbp-96], xmm0
movsd xmm0, [rbp-72]
addsd xmm0, [rbp-96]
movsd [rbp-64], xmm0
movsd xmm0, [rbp-16]
addsd xmm0, [rbp-32]
movsd [rbp-112], xmm0
movsd xmm0, [rbp-112]
addsd xmm0, [rbp-48]
movsd [rbp-104], xmm0
movsd xmm0, [rbp-64]
divsd xmm0, [rbp-104]
movsd [rbp-56], xmm0
movsd xmm0, [rbp-56]
leave
ret
MATLAB
function result = weighted_mean(v1, a, v2, b, v3, c)
result = ((((v1 * a) + (v2 * b)) + (v3 * c)) / ((a + b) + c));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[v1_, a_, v2_, b_, v3_, c_] := ((((v1 * a) + (v2 * b)) + (v3 * c)) / ((a + b) + c));
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 textbookCite 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). Weighted Mean Calculator. MW SysArc Tools. https://math.mwsysarc.com/statistics/weighted-mean-calculator
MLA 9
MW SysArc. “Weighted Mean Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/statistics/weighted-mean-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Weighted Mean Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/statistics/weighted-mean-calculator.
Harvard
MW SysArc (2026) ‘Weighted Mean Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/statistics/weighted-mean-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_weighted_mean_2026,
author = {{MW SysArc}},
title = {Weighted Mean Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/statistics/weighted-mean-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Weighted Mean Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/statistics/weighted-mean-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Weighted mean do?
Calculate the weighted mean of three values when observations have different importance or frequency.
How does the Weighted mean work?
The calculator applies Weighted mean = Σ(wx) ÷ Σw. Each value contributes in proportion to its weight, so larger weights exert more influence on the mean.
What can I learn from the Weighted mean?
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 .