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up vote 6 down vote favorite

I would like to use LaTeX 3 to automatically calculate the median of a set of predefined data.

Consider the following example:

\documentclass{article}

\def\waterAa{82}
\def\waterAb{51}
\def\waterAc{144}
\def\waterAd{84}
\def\waterAe{120}
\def\waterAf{148}
\def\waterAg{148}
\def\waterAh{108}
\def\waterAi{160}
\def\waterAj{86}

\begin{document}

\noindent Consider the data set
\begin{equation}
  \{\waterAa, \waterAb, \waterAc, \waterAd, \waterAe, \waterAf, \waterAg, \waterAh, \waterAi, \waterAj\}
\end{equation}
To find the median of a data set, we first have to arrange the elements relative to their values:
\begin{equation}
  \{\waterAb, \waterAa, \waterAd, \waterAj, \waterAh, \waterAe, \waterAc, \waterAf, \waterAg, \waterAi\}
\end{equation}
Since the number of elements is $10$, the median~$M$ is the average of the fifth and sixth element:
\begin{equation}
  M = (\waterAh+\waterAe)/2 = 114.
\end{equation}

\section*{Question}
How to I \emph{automatically} calculate the median of a data set (preferably using \LaTeX 3)?

\end{document}

question

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up vote 4 down vote accepted

You can use floating point numbers; the trick is to expand the values when absorbing them.

\documentclass{article}

\usepackage{xparse}
\usepackage{l3sort}

\ExplSyntaxOn

\NewDocumentCommand{\median}{m}
 {
  \svend_median:x { #1 }
 }

\clist_new:N \l__svend_median_clist
\int_new:N \l__svend_median_int

\cs_new_protected:Nn \svend_median:n
 {
  % set a comma separated list
  \clist_set:Nn \l__svend_median_clist { #1 }
  % sort it numerically
  \clist_sort:Nn \l__svend_median_clist
   {
    \fp_compare:nTF { ##1 > ##2 }
     { \sort_reversed: }
     { \sort_ordered: }
   }
  % compute the number of items
  \int_set:Nn \l__svend_median_int { \clist_count:N \l__svend_median_clist }
  \int_if_odd:nTF {\l__svend_median_int }
   {% if the number is odd, return the middle item
    \clist_item:Nn \l__svend_median_clist { (\l__svend_median_int + 1)/2 }
   }
   {% otherwise the average of the middle two elements
    \fp_eval:n
     {
      ( 
       \clist_item:Nn \l__svend_median_clist { \l__svend_median_int/2 }
       +
       \clist_item:Nn \l__svend_median_clist { \l__svend_median_int/2 + 1 }
      )/2
     }
   }
 }
\cs_generate_variant:Nn \svend_median:n { x }
\ExplSyntaxOff

\begin{document}

\def\waterAa{82}
\def\waterAb{51}
\def\waterAc{144}
\def\waterAd{84}
\def\waterAe{120}
\def\waterAf{148}
\def\waterAg{148}
\def\waterAh{108}
\def\waterAi{160}
\def\waterAj{86}


The median is \median{82,51,144,84,120,148,148,108,160,86}

The median is \median{
  \waterAa, \waterAb, \waterAc, \waterAd, \waterAe, 
  \waterAf, \waterAg, \waterAh, \waterAi, \waterAj
}

The median is \median{
  \waterAa, \waterAb, \waterAc, \waterAd, \waterAe, 
  \waterAf, \waterAg, \waterAh, \waterAi, %\waterAj
}

The median is \median{1,2,3,4}

The median is \median{1,2,3}

The median is \median{3.3,4.4,5.503,6.01}

The median is \median{3.3,4.4,5.503}

\end{document}

enter image description here

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up vote 7 down vote

Luckily, there is l3sort for sorting the sequence of numbers (I assumed integer values only here)

The rest is just code to determine the middle position of the indices. As it stands, the code is not expandable, however, since \seq_sort:Nn is not expandable and the \int_set:Nn prevents expansion as well. 

\documentclass{article}

\usepackage{xparse}
\usepackage{l3sort}

\ExplSyntaxOn

\cs_generate_variant:Nn \seq_item:Nn {NV}

\NewDocumentCommand{\median}{m}{%
  \seq_set_from_clist:Nn \l_tmpa_seq {#1}
  \seq_sort:Nn \l_tmpa_seq {%
    \int_compare:nNnTF { ##1 } > { ##2 }
    { \sort_reversed: }
    { \sort_ordered: }
  }
  \int_set:Nn \l_tmpa_int {\seq_count:N \l_tmpa_seq }
  \int_if_odd:nTF { \l_tmpa_int } {%
    \int_set:Nn \l_tmpb_int {\l_tmpa_int / 2}
    \int_set:Nn \l_tmpa_int {\l_tmpb_int}
  }{%
    \int_set:Nn \l_tmpb_int {\l_tmpa_int / 2 }
    \int_set:Nn \l_tmpa_int {\l_tmpb_int + 1}
  }
  \fp_eval:n {(\seq_item:NV \l_tmpa_seq \l_tmpb_int + \seq_item:NV \l_tmpa_seq \l_tmpa_int)/2}
}

\ExplSyntaxOff

\begin{document}

\def\waterAa{82}
\def\waterAb{51}
\def\waterAc{144}
\def\waterAd{84}
\def\waterAe{120}
\def\waterAf{148}
\def\waterAg{148}
\def\waterAh{108}
\def\waterAi{160}
\def\waterAj{86}


The median is \median{82,51,144,84,120,148,148,108,160,86}

The median is \median{\waterAa, \waterAb, \waterAc, \waterAd, \waterAe, \waterAf, \waterAg, \waterAh, \waterAi, \waterAj}

\end{document}

enter image description here

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