<?xml version="1.0" encoding="ISO-8859-1" standalone="no"?>
<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>variancef</TITLE>
  <TYPE>  </TYPE>
  <DATE>July 2000</DATE>
  <SHORT_DESCRIPTION name="variancef"> standard deviation of the values of a  vector or matrix</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>s=variancef(x,fre)  </CALLING_SEQUENCE_ITEM>
    <CALLING_SEQUENCE_ITEM>s=variancef(x,fre,'r') or s=variancef(x,fre,1)  </CALLING_SEQUENCE_ITEM>
    <CALLING_SEQUENCE_ITEM>s=variancef(x,fre,'c') or s=variancef(x,fre,2)  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>x</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: real or complex vector or matrix</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
    This  function computes the variance  of the values of a
    vector  or matrix <VERB>x</VERB>,  each of  them counted with a
    frequency  signaled by  the corresponding values  of the
    integer vector or matrix <VERB>fre</VERB> with the same type of
    <VERB>x</VERB>.</P>
    <P>
    For a vector  or matrix <VERB>x</VERB>, <VERB>s=variancef(x,fre)</VERB> (or
    <VERB>s=variancef(x,fre,'*')</VERB>)  returns in scalar <VERB>s</VERB>  the
    variance of all  the   entries of <VERB>x</VERB>, each    value
    counted  with   the    multiplicity  indicated by    the
    corresponding value of <VERB>fre</VERB>.</P>
    <P><VERB>s=variancef(x,fre,'r')</VERB>(or,                equivalently,
    <VERB>s=variancef(x,fre,1)</VERB>) returns in each  entry of the row
    vector  <VERB>s</VERB> of  type  1xsize(x,'c') the  variance of
    each column of  <VERB>x</VERB>,   each value counted  with  the
    multiplicity  indicated by  the  corresponding value  of
    <VERB>fre</VERB>.</P>
    <P><VERB>s=variancef(x,fre,'c')</VERB>(or,                equivalently,
    <VERB>s=variancef(x,fre,2)</VERB>)  returns  in  each   entry of the
    column vector <VERB>s</VERB> of type size(x,'c') x1 the variance
    of  each row  of  <VERB>x</VERB>, each value  counted  with the
    multiplicity indicated  by  the  corresponding value  of
    <VERB>fre</VERB>.</P>
  </DESCRIPTION>
  <EXAMPLE>
<![CDATA[

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')

 ]]>
  </EXAMPLE>
  <AUTHOR> Carlos Klimann</AUTHOR>
  <BIBLIO>
    <P>
    Wonacott, T.H. &amp; Wonacott, R.J.; Introductory Statistics, fifth edition, J.Wiley &amp; Sons, 1990.</P>
  </BIBLIO>
</MAN>
