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)




Arguments
~~~~~~~~~

: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')




Bibliography
~~~~~~~~~~~~

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