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# variance

variance of the values of a vector or matrix (or hypermatrix) real or complex

### Calling Sequence

s = variance(x [,orien [,w]]) s = variance(x,'r') or s = variance(x,1) s = variance(x,'c') or s = variance(x,2) s = variance(x,'*',1) s = variance(x,'r',1) s = variance(x,'c',1)

### Arguments

- x
real or complex vector or matrix. An hypermatrix is accepted only for undirectional computations

`variance(x)`

or`variance(x,"*",1)`

- orien
the orientation of the computation. Valid values are

- 1 or "r" : result is a row, after a column-wise computation.
- 2 or "c" : result is a column, after a row-wise computation.
- "*" : full undirectional computation (default); useful explicitly when
`w`

is used.

- w
w : type of normalization to use. Valid values are

- 0 : provides the best unbiased estimator of the variance when the mean is not known a priori. This is the default. The sum is normalized by 1/(nE-1), where nE is the number of summed elements (the number of rows nR if "r" is used; of columns nC if "c" is used; or by default nC*nR)
- 1 : provides the second moment around the mean. The sum is normalized by 1/nE. This estimation is unbiased only if the mean is known a priori.

### Description

This function computes the variance of the real or complex numbers stored into a vector or matrix `x`

. If `x`

is complex, `variance(x,..) = variance(real(x),..) + variance(imag(x),..)`

is returned.

For a vector, a matrix, or an hypermatrix `x`

, `s = variance(x)`

or `s = variance(x, "*", 1)`

returns in the scalar `s`

the variance of all the entries of `x`

.

`s = variance(x,'c')`

(or, equivalently, `s = variance(x,2)`

)
is the columnwise variance: s is a column vector, with `s(j) = variance(x(j,:))`

.

`s = variance(x,'r')`

(or, equivalently, `s = variance(x,1)`

)
is the rowwise variance: s is a row vector, with s(i) the variance of `s(i) = variance(x(:,i))`

.

### Examples

x = [ 0.2113249 0.0002211 0.6653811;0.7560439 0.4453586 0.6283918 ] s = variance(x) s = variance(x, "r") s = variance(x, "c") // with complex numbers x = rand(4,3) + rand(4,3)*%i s = variance(x) s = variance(x, "*", 1) // should be smaller than the previous one s = variance(x, "r") s = variance(x, "r", 1) s = variance(x, "c") // with an hypermatrix x = rand(3,2,2) s = variance(x) s = variance(x, "*", 1) // should be smaller than the previous one // s = variance(x, "r") // is not supported for an hypermatrix // s = variance(x, "c") // is not supported for an hypermatrix

### See Also

- mtlb_var — Matlab var emulation function

### Bibliography

Wonacott, T.H. & Wonacott, R.J.; Introductory Statistics, fifth edition, J.Wiley & Sons, 1990.

### History

Version | Description |

5.4.1 | variance(complexes) fixed. variance(x,"*",1) introduced. Vectorization of the code for directional usages variance(x,"r"|"c"). Full revision of the help page |

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