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Arithmetic Mean

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

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Arithmetic Mean -

Tag(s) : Mathematics, Data processing

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Arithmetic Mean

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

Answers to Questions

How to compute an 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.

How to code an arithmetic mean (source code)?

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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Source code

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