VAR Variance Function

Section: Elementary Functions

Usage

Computes the variance of an array along a given dimension. The general syntax for its use is 
  y = var(x,d)

where x is an n-dimensions array of numerical type. The output is of the same numerical type as the input. The argument d is optional, and denotes the dimension along which to take the variance. The output y is the same size as x, except that it is singular along the mean direction. So, for example, if x is a 3 x 3 x 4 array, and we compute the mean along dimension d=2, then the output is of size 3 x 1 x 4.

Function Internals

The output is computed via

where

If d is omitted, then the mean is taken along the first non-singleton dimension of x.

Example

The following piece of code demonstrates various uses of the var function 
--> A = [5,1,3;3,2,1;0,3,1]

A = 
 5 1 3 
 3 2 1 
 0 3 1

We start by calling var without a dimension argument, in which case it defaults to the first nonsingular dimension (in this case, along the columns or d = 1). 

--> var(A)

ans = 
    6.3333    1.0000    1.3333

Next, we take the variance along the rows. 

--> var(A,2)

ans = 
    4.0000 
    1.0000 
    2.3333