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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

## Weighted (Arithmetic) Mean Calculator

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.

### 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 }