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) : Statistics, Data Processing

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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`

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Cite as source (bibliography):

*Mean of Numbers* on dCode.fr [online website], retrieved on 2024-09-14,

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

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