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# var() - Signal Processing

```V = var(A) returns
the variance of the
elements of A along the first array dimension whose
size does not equal 1. If A is a vector of observations,
the variance is a scalar.If A is a matrix whose columns
are random variables and whose rows are observations, V is
a row vector containing the variances corresponding to each column.If A is a multidimensional array,
then var(A) treats the values along the first array
dimension whose size does not equal 1 as vectors. The size of this
dimension becomes 1 while the sizes of all other
dimensions remain the same.The variance is normalized by the number of observations-1 by
default.If A is a scalar, var(A) returns 0.
If A is a 0-by-0 empty
array, var(A) returns NaN.exampleV = var(___,w) specifies
a weighting scheme for any of the previous syntaxes. When w
= 0 (default), V is normalized by the
number of observations-1. When w = 1,
it is normalized by the number of observations. w can
also be a weight vector containing nonnegative elements. In this case,
the length of w must equal the length of the dimension
over which var is operating. exampleV = var(___,dim) returns
the variance along the dimension dim for any of
the previous syntaxes. To maintain the default normalization while
specifying the dimension of operation, set w = 0 in
the second argument.exampleV = var(___,nanflag) specifies
whether to include or omit NaN values from the
calculation for any of the previous syntaxes. For example, var(A,'includenan') includes
all NaN values in A while var(A,'omitnan') ignores
them.```

### Syntax

`V = var(A) exampleV = var(___,w) exampleV = var(___,dim) exampleV = var(___,nanflag) example`

### Example

```Variance of MatrixOpen This ExampleCreate a matrix and compute its variance.A = [4 -7 3; 1 4 -2; 10 7 9];
var(A)

ans =

21.0000   54.3333   30.3333

Variance of ArrayOpen This ExampleCreate a 3-D array and compute its variance.A(:,:,1) = [1 3; 8 4];
A(:,:,2) = [3 -4; 1 2];
var(A)

ans(:,:,1) =

24.5000    0.5000

ans(:,:,2) =

2    18

Specify Variance Weight VectorOpen This ExampleCreate a matrix and compute its variance according to a weight vector w.A = [5 -4 6; 2 3 9; -1 1 2];
w = [0.5 0.25 0.25];
var(A,w)

ans =

6.1875    9.5000    6.1875

Specify Dimension for VarianceOpen This ExampleCreate a matrix and compute its variance along the first dimension.A = [4 -2 1; 9 5 7];
var(A,0,1)

ans =

12.5000   24.5000   18.0000

Compute the variance of A along the second dimension.var(A,0,2)

ans =

9
4

Variance Excluding NaNOpen This ExampleCreate a vector and compute its variance, excluding NaN values.A = [1.77 -0.005 3.98 -2.95 NaN 0.34 NaN 0.19];
V = var(A,'omitnan')

V =

5.1970```