Last update : 00/00/0000

variancef - standard deviation of the values of a vector or matrix

### Calling Sequence

  `s=variancef(x,fre)`
  `s=variancef(x,fre,'r') or s=variancef(x,fre,1)`
  `s=variancef(x,fre,'c') or s=variancef(x,fre,2)`

### Parameters

- `x`: real or complex vector or matrix

### Description

This function computes the variance of the values of a vector or matrix `x`, each of them counted with a frequency signaled by the corresponding values of the integer vector or matrix `fre` with the same type of `x`.

For a vector or matrix `x`, `s=variancef(x,fre)` (or `s=variancef(x,fre,'*')`) returns in scalar `s` the variance of all the entries of `x`, each value counted with the multiplicity indicated by the corresponding value of `fre`.

`s=variancef(x,fre,'r')`(or, equivalently, `s=variancef(x,fre,1)`) returns in each entry of the row vector `s` of type 1xsize(x,'c') the variance of each column of `x`, each value counted with the multiplicity indicated by the corresponding value of `fre`.

`s=variancef(x,fre,'c')`(or, equivalently, `s=variancef(x,fre,2)`) returns in each entry of the column vector `s` of type size(x,'c') x1 the variance of each row of `x`, each value counted with the multiplicity indicated by the corresponding value of `fre`.

### Examples

    x=[0.2113249 0.0002211 0.6653811;0.7560439 0.9546254 0.6283918]
    fre=[1 2 3;3 4 3]
    m=variancef(x,fre)
    m=variancef(x,fre,'r')
    m=variancef(x,fre,'c')

### Author

Carlos Klimann

### Bibliography

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