Tool to compute a mean from numbers. The arithmetic mean (or commonly the mean/average) of a list of numbers is a statistical representation showing the distribution of the numbers in the list.

Arithmetic Mean - dCode

Tag(s) : Statistics, Data Processing

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⮞ Go to: Mean of a Function

⮞ Go to: Weighted Mean of Numbers

The **arithmetic mean** is the mathematical term to define what is commonly called *mean* or *>average.*

Take a list of $ n $ values (digits, numbers, natural or real numbers) $ X = \{x_1, x_2, \dots, x_n \} $. The **arithmetic mean** is defined by the sum of the values divided by the number of values $ n $.

$$ \bar{x} = {1 \over n} \ sum_{i=1}^n{x_i} $$

The **arithmetic mean** is generally used to give a general trend to a set of homogeneous data, possibly bounded, for example school marks between 0 and 20.

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

This definition can be extended to a function, see function mean calculator.

To find the central value of a list, see median calculator.

When the values are assigned coefficients, see the weighted mean calculator.

For a list of $ n $ values $ X = \{x_1, x_2, \dots, x_n\} $ having a mean $ \bar {x} = m $, two possible scale changes:

If all $ x_i $ are increased by $ a $ then the **arithmetic mean** is also increased by $ a $ and becomes $ \bar{x} = m + a $

If all $ x_i $ are multiplied by $ a $ then the **arithmetic mean** is also multiplied by $ a $ and becomes $ \bar{x} = m \times a $

Classic method:` // pseudocode`

function mean(array[N]) {

sum = 0

for i = 0; i < N ; i++ {

sum += array[i]

}

return sum / N

}

Optimized method for floats (avoid big values) :` // pseudocode`

function mean(array[N]) {

m = 0

for i = 0; i < N; i++) {

m += (array[i] - m)/(i+1);

}

return m

}

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