Tool to calculate the different means of a number list. The mathematic mean of a list of numbers is one of the statistical representations that can illustrate the distribution of the numbers in the list.

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*!

Tool to calculate the different means of a number list. The mathematic mean of a list of numbers is one of the statistical representations that can illustrate the distribution of the numbers in the list.

For a list of $ n $ values $ X = \{x_1, x_2, \dots, x_n \} $. The arithmetic mean has for definition the sum of all the values divided by the number count of values $ n $. $$ \bar{x} = {1 \over n} \ sum_{i=1}^n{x_i} $$

__Example:__ The list of 4 numbers 12, 14, 18, 13 its** average** value is (12+14+18+13)/4=14.25

When values are associaed with coefficients (digits or numbers), then use the weighted arithmetic mean.

For a list of $ n $ values $ X = \{x_1, x_2, \dots, x_n \} $. The geometric mean has for definition the $ n $-th root of the product of values. $$ \bar{x}_{geom} = \sqrt[n]{\prod_{i=1}^n{x_i}} $$

The geometric mean is often used to calculate an** average** interest rate.

__Example:__ The list of 3 values 1, 1.5, 2 has for geometric mean $ \sqrt[3]{ 1 \times 1.5 \times 2 } \approx 1.4422 $

For a list of n values $ X = \{x_1, x_2, \dots, x_n \} $. The harmonic mean has for definition the ratio of n to the sum of the inverse of the values. $$ \bar{x}_{harm} = \frac{n}{\sum_{i=1}^n \frac{1}{x_i}} $$

The harmonic mean is often used to compute a speed** average**.

__Example:__ The list of speed values 50 and 100 has for harmonic mean $ 2/(1/50+1/100) = 66.67 $

For a list of n values $ X = \{x_1, x_2, \dots, x_n \} $. The root mean square (or quadratic mean) has for definition the root of the sum of each value squared, divided by root of n: $$ \bar{x}_{quad} = \sqrt{\frac{1}{n}\sum_{i=1}^n{x_i^2}} $$

The RMS is used in electricity to calculate the effective value.

__Example:__ The list of 3 values 4,5 and 6, this distribution has for quadratic mean $ \sqrt{\frac{4^2+5^2+6^2}{3}} = \approx 5.06 $

It is impossible to find the original numbers from the** mean value**. There are endless lists of possible numbers with the same** mean value**.

__Example:__ 10,20,30 has the same arithmetic mean as -100,0,1,99,100

dCode retains ownership of the source code of the script Mean of Numbers online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Mean of Numbers script for offline use on PC, iPhone or Android, ask for price quote on contact page !

mean,average,number,digit,arithmetic,harmonic,geometric,proportional,quadratic,weighted,list,distribution

Source : https://www.dcode.fr/mean

© 2020 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.

Feedback

▲