## VAR Variance Function

Section: Elementary Functions

### Usage

Computes the variance of an array along a given dimension. The general syntax for its use isy = 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