Tool to calculate weighted means. The weighted mean of a statistical value related to a list of numbers that are associated with a coefficient: their weight.

Weighted Mean of Numbers - dCode

Tag(s) : Mathematics, Data Processing

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!

A suggestion ? a feedback ? a bug ? an idea ? *Write to dCode*!

The weighted mean of a statistical value related to a list of numbers that are associated with a coefficient: their weight, a number which therefore takes up more or less value in the calculated mean.

Take a list of $ n $ values $ X = \{x_1, x_2, \dots, x_n\} $ associated with weights $ W = \{ w_1, w_2, \dots, w_n\} $. The **weighted arithmetic mean** is defined by the sum of values multiplied by their weight, divided by the sum of weights. Formula: $$ \bar{x} = \frac{ \sum_{i=1}^n w_i x_i}{\sum_{i=1}^n w_i} $$

__Example:__ The list of 3 numbers $ 12 $ (coefficient $ 7 $), $ 14 $ (coefficient $ 2 $) and $ 16 $ (coefficient $ 1 $) has for weighted mean $ (12 \times 7 + 14 \times 2 + 16 \times 1) / (7 + 2 + 1) = 12.8 $

Take a list of n values $ X = \{x_1, x_2, \dots, x_n\} $ associated with weights $ W = \{ w_1, w_2, \dots, w_n\} $. The **weighted geometric mean** is defined by the pth root of the product of values, where p is the weight's sum. Formula: $$ \bar{x}^G = \left(\prod_{i=1}^n x_i^{w_i}\right)^{1 / \sum_{i=1}^n w_i} = \quad \exp \left( \frac{1}{\sum_{i=1}^n w_i} \; \sum_{i=1}^n w_i \ln x_i \right) $$

Take a list of n values $ X = \{x_1, x_2, \dots, x_n\} $ associated with weights $ W = \{ w_1, w_2, \dots, w_n\} $. The **weighted harmonic mean** is defined by the ratio of p (the weight sum) to the sum of the ratio of each weigth over the values. Formula: $$ \bar{x}^H = \sum_{i=1}^n w_i \bigg/ \sum_{i=1}^n \frac{w_i}{x_i} $$

dCode retains ownership of the "Weighted Mean of Numbers" source code. Except explicit open source licence (indicated Creative Commons / free), the "Weighted Mean of Numbers" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Weighted Mean of Numbers" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Weighted Mean of Numbers" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!

Reminder : dCode is free to use.

The copy-paste of the page "Weighted Mean of Numbers" or any of its results, is allowed (even for commercial purposes) as long as you cite dCode!

Exporting results as a .csv or .txt file is free by clicking on the *export* icon

Cite as source (bibliography):

*Weighted Mean of Numbers* on dCode.fr [online website], retrieved on 2023-12-06,

moyenne,weighted,pondered,nombre,chiffre,arithmetic,harmonic,geometric,proportional,list

https://www.dcode.fr/weighted-mean

© 2023 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.

Feedback