Arithmetic Mean

The arithmetic mean is the mathematical term to define what is simply called mean or average.

Consider 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.

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
}