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Arithmetic Mean

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.

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Arithmetic Mean -

Tag(s) : Statistics, Data Processing

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Arithmetic Mean

Mean Calculator

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Arithmetic Mean of a Function Calculator

Weighted (Arithmetic) Mean Calculator

Answers to Questions (FAQ)

How to compute an arithmetic mean?

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.

How to change of scale an arithmetic mean?

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 $

How to calculate the average of 2 lists knowing their means?

To perform a sort of addition of an average of 2 lists: a list $ A $ of $ n_1 $ values and average $ \bar {A} = m_1 $ and a list $ B $ of $ n_2 $ values and average $ \bar {B} = m_2 $, then the average of the 2 lists is given by the formula:

$$ \overline{A+B} = \frac{n_1 m_1 + n_2 m_2}{n_1+n_2} $$

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
}

Source code

dCode retains ownership of the online 'Arithmetic Mean' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any 'Arithmetic Mean' algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any 'Arithmetic Mean' function (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and no data download, script, copy-paste, or API access for 'Arithmetic Mean' will be for free, same for offline use on PC, tablet, iPhone or Android ! dCode is free and online.

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