## 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