scilab/modules/statistics/help/en_US/3_dispersion_widths/mad.xml

   1 <?xml version="1.0" encoding="UTF-8"?>
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  16 <refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="mad">
  17     <refnamediv>
  18         <refname>mad</refname>
  19         <refpurpose>mean absolute deviation</refpurpose>
  20     </refnamediv>
  21     <refsynopsisdiv>
  22         <title>Syntax</title>
  23         <synopsis>s2=mad(x)
  24             s2=mad(x,'r') or s2=mad(x,1)
  25             s2=mad(x,'c') or s2=mad(x,2)
  26         </synopsis>
  27     </refsynopsisdiv>
  28     <refsection>
  29         <title>Arguments</title>
  30         <variablelist>
  31             <varlistentry>
  32                 <term>x</term>
  33                 <listitem>
  34                     <para>real or complex vector or matrix</para>
  35                 </listitem>
  36             </varlistentry>
  37         </variablelist>
  38     </refsection>
  39     <refsection>
  40         <title>Description</title>
  41         <para>
  42             This function computes   the mean absolute deviation of  a
  43             real or complex vector or matrix <literal> x</literal>.
  44         </para>
  45         <para>
  46             For  a  vector  or matrix  <literal>   x</literal>, <literal> s2=mad(x)  </literal>
  47             returns in scalar <literal> s2</literal> the mean absolute  deviation
  48             of all the entries of <literal> x</literal>.
  49         </para>
  50         <para>
  51             <literal> s2=mad(x,'r')  </literal> (or, equivalently,  <literal> s2=mad(x,1)</literal>)
  52             returns in each entry of the column vector <literal> s2</literal>
  53             the mean absolute deviation of each column of <literal> x</literal>.
  54         </para>
  55         <para>
  56             <literal> s2=mad(x,'c')  </literal> (or, equivalently,  <literal> s2=mad(x,2)</literal>)
  57             returns in each entry of the column vector <literal> s2</literal>
  58             the mean absolute deviation of each row of <literal> x</literal>.
  59         </para>
  60     </refsection>
  61     <refsection>
  62         <title>Examples</title>
  63         <programlisting role="example"><![CDATA[
  64 x  = [2 2 3 4 14];
  65
  66 // Mean absolute deviation of a set of data
  67 // Expected = (|2-5|+|2-5|+|3-5|+|4-5|+|14-5|) / 5 = 3.6
  68 mad(x)
  69    ]]></programlisting>
  70     </refsection>
  71     <refsection>
  72         <title>Bibliography</title>
  73         <para>
  74             Reference: Wonacott  T.H.&amp; Wonacott  R.J. .-  Introductory Statistics, 5th edition, John Wiley, 1990.
  75         </para>
  76     </refsection>
  77 </refentry>