variance Interface

public interface variance

Calculates the sample variance of a set of values given in a vector of any size with one dimension applying the following equation:

$$\sigma^{2} = \frac{\sum\limits_{i=1}^{n}\left(x_{i} - \overline{x}\right)^2}{n-1}$$

Where:

• $x$ is a vector with real numbers.
• $n$ is how many numbers are included in $x$.

Syntax

y = variance(x)

Where:

• x = vector of rank 1 with real numbers. See this example to use an array of rank larger than 1.
• y = real number of the same kind as x with the sample variance of x.

Example

The following program calculates the variance of a vector:

 PROGRAM varianceExample
    USE FU_Statistics, ONLY: variance
    IMPLICIT NONE
    REAL, DIMENSION(5) :: x = [1., 2., 3., 4., 5.]
    WRITE(*,*) variance(x)
 END PROGRAM varianceExample

Module Procedures