Mean (Average) - Statistical Concepts

Concept

Mean or Average is used widely in machine learning starting from algorithms to evaluation and optimizations. It is simply an average of a set of values. It is usually denoted by \(\bar{x}\) (x bar). Let’s understand the formula and an example.

Formula

$$ \bar{x}=\frac{1}{n}\left(\sum_{i=1}^{n} x_{i}\right)=\frac{x_{1}+x_{2}+\cdots+x_{n}}{n} $$

Here \( \sum \) = symbol for doing summation of values,
x is a value from a table, dataset, or simply from a set of values,
n is a number of values in a table, dataset, or set of values.

Explanation

You might have got it already, we are simply doing a sum of all the values and diving it by the number of values. The result of this computation is a mean or an average of all the values.

It is used in different evaluation metrics and machine learning algorithms. Let’s jump on to one example quickly.

Example

Here in this table n = 9

Putting it in our formula:

$$ \bar{x}=\frac{1}{n}\left(\sum_{i=1}^{n} x_{i}\right)=\frac{x_{1}+x_{2}+\cdots+x_{n}}{n} $$

$$ \bar{x}=\frac{103.6}{9} = 11.51 $$

11.51 will be our mean of all the values from a table.