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Вычисление среднего значения в (La)TeX

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Вычисление среднего значения в (La)TeX

У меня есть список отметок, включенных в .texдокумент, с begin{filecontents*}командой.

Пока что я рисую гистограмму частот встречаемости отметок.

Я хотел бы добавить среднее значение.

Можете ли вы мне помочь? Вот мой код на данный момент,адаптировано из этого ответа

\documentclass[a4paper, landscape]{article}


\usepackage{filecontents}
\begin{filecontents*}{commadata.dat}
8,5
13,5
6,5
8,5
10
8
5,5
2,5
5,5
7
20
12
18,5
5,5
9,5
3,5
0
7
7
5,5
10
3,5
7
14,5
7
10,5
16,5
10,5
6,5
8
14
8,5
2,5
5
9,5
8
10
9,5
9
8,5
4,5
5,5
\end{filecontents*}


%%%%%%%%%%
% Layout %
%%%%%%%%%%
\def\myHMargin{0.85cm}
\def\myVMarginTop{7mm}
\def\myVMarginBottom{7mm}
\usepackage[hmargin={\myHMargin,\myHMargin},
            vmargin={\myVMarginTop,\myVMarginBottom},
            headsep=5mm,
            footskip=\dimexpr(\baselineskip+4mm),
            includefoot,
            includehead,
            twoside]{geometry}
\pagestyle{empty}

\usepackage{xstring}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{pgfplots}
\pgfplotsset{compat=1.14}
\newcommand*{\ReadOutElement}[4]{%
    \pgfplotstablegetelem{#2}{[index]#3}\of{#1}%
    \let#4\pgfplotsretval
}


%----------------------------------------------------------------------------
\begin{document}
%----------------------------------------------------------------------------



% grid style
\pgfplotsset{grid style={dotted,gray}}


\begin{center}

\fbox{Mean value : $\displaystyle\frac{\ ??? \ }{20}$}

 \begin{tikzpicture}
  \pgfplotstableread[/pgf/number format/read comma as period]{commadata.dat}\datatable
  \pgfplotstablegetrowsof{\datatable}
  \pgfmathtruncatemacro{\numrows}{\pgfplotsretval}
  \pgfplotstablegetcolsof{\datatable}
  \pgfmathtruncatemacro{\numcols}{\pgfplotsretval}

%  \edef\myxmax{0}%
%  \foreach \nY in {1,...,\numrows}
%  {\ReadOutElement{\datatable}{\the\numexpr\nY-1}{0}{\Current}%
%   \StrSubstitute{\Current}{,}{.}[\mytemp]
%   \pgfmathtruncatemacro{\myx}{\mytemp}
%   \pgfmathtruncatemacro{\myxmax}{max(\myxmax,\myx)}
%   \xdef\myxmax{\myxmax}
%  }

  \edef\myxmax{20}
  \foreach \X in {0,...,\myxmax}
  {\expandafter\xdef\csname mypile\X\endcsname{0}}
  \foreach \nY in {1,...,\numrows}
  {\ReadOutElement{\datatable}{\the\numexpr\nY-1}{0}{\Current}%
   \StrSubstitute{\Current}{,}{.}[\mytemp]
   \pgfmathtruncatemacro{\myx}{\mytemp}%
   \edef\currentval{\csname mypile\myx\endcsname}
   \pgfmathtruncatemacro{\mycur}{\currentval+1}
   \expandafter\xdef\csname mypile\myx\endcsname{\mycur}
  }

  \begin{axis}[ymajorgrids,
        ymin=0,% ymax=6.2,
        xmin=-1,
        %ytick={0,2,...,6},
        xtick={0,1,...,20},
        xticklabels={\small $0$-$1$, \small $1$-$2$, \small $2$-$3$, \small $3$-$4$, \small $4$-$5$, \small $5$-$6$, \small $6$-$7$, \small $7$-$8$, \small $8$-$9$, \small $9$-$10$, \small $10$-$11$, \small $11$-$12$, \small 
        $12$-$13$, \small $13$-$14$, \small $14$-$15$, \small $15$-$16$, \small $16$-$17$, \small $17$-$18$, \small $18$-$19$, \small $19$-$20$, \small $\geq 20$},
        minor y tick num = 0,
        %area style,
        width=28cm,
        height=10cm,
        axis lines*=left,
        %bar width=0.2cm,
        y axis line style = {->},
        x axis line style = {->},
        tick align      = outside,
        tick pos        = left
        ]
   \pgfplotsinvokeforeach{0,...,\myxmax}{%
   \edef\currentval{\csname mypile#1\endcsname}
   \pgfmathtruncatemacro{\mycur}{\currentval}
   \addplot[ybar, fill=black!20, draw=black!40, ycomb, line width=8mm, color=blue!50] coordinates {(#1,\mycur)};
   }    
  \end{axis}
 \end{tikzpicture}
\end{center}



\end{document}

введите описание изображения здесь

решение1

Что-то вроде этого?

\documentclass[a4paper, landscape]{article}


\usepackage{filecontents}
\begin{filecontents*}{commadata.dat}
8,5
13,5
6,5
8,5
10
8
5,5
2,5
5,5
7
20
12
18,5
5,5
9,5
3,5
0
7
7
5,5
10
3,5
7
14,5
7
10,5
16,5
10,5
6,5
8
14
8,5
2,5
5
9,5
8
10
9,5
9
8,5
4,5
5,5
\end{filecontents*}


%%%%%%%%%%
% Layout %
%%%%%%%%%%
\def\myHMargin{0.85cm}
\def\myVMarginTop{7mm}
\def\myVMarginBottom{7mm}
\usepackage[hmargin={\myHMargin,\myHMargin},
            vmargin={\myVMarginTop,\myVMarginBottom},
            headsep=5mm,
            footskip=\dimexpr(\baselineskip+4mm),
            includefoot,
            includehead,
            twoside]{geometry}
\pagestyle{empty}

\usepackage{xstring}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{pgfplots}
\pgfplotsset{compat=1.14}
\newcommand*{\ReadOutElement}[4]{%
    \pgfplotstablegetelem{#2}{[index]#3}\of{#1}%
    \let#4\pgfplotsretval
}


%----------------------------------------------------------------------------
\begin{document}
%----------------------------------------------------------------------------



% grid style
\pgfplotsset{grid style={dotted,gray}}


\begin{center}

%\fbox{Mean value : $\displaystyle\frac{\ ??? \ }{20}$}

 \begin{tikzpicture}
  \pgfplotstableread[/pgf/number format/read comma as period]{commadata.dat}\datatable
  \pgfplotstablegetrowsof{\datatable}
  \pgfmathtruncatemacro{\numrows}{\pgfplotsretval}
  \pgfplotstablegetcolsof{\datatable}
  \pgfmathtruncatemacro{\numcols}{\pgfplotsretval}

  \edef\myxmax{20}
  \foreach \X in {0,...,\myxmax}
  {\expandafter\xdef\csname mypile\X\endcsname{0}}
  \edef\Total{0}
  \foreach \nY in {1,...,\numrows}
  {\ReadOutElement{\datatable}{\the\numexpr\nY-1}{0}{\Current}%
   \StrSubstitute{\Current}{,}{.}[\mytemp]
   \pgfmathtruncatemacro{\myx}{\mytemp}%
   \pgfmathsetmacro{\Total}{\Total+\myx}
   \xdef\Total{\Total}
   \edef\currentval{\csname mypile\myx\endcsname}
   \pgfmathtruncatemacro{\mycur}{\currentval+1}
   \expandafter\xdef\csname mypile\myx\endcsname{\mycur}
  }
  \begin{axis}[ymajorgrids,
        ymin=0,% ymax=6.2,
        xmin=-1,
        %ytick={0,2,...,6},
        xtick={0,1,...,20},
        xticklabels={\small $0$-$1$, \small $1$-$2$, \small $2$-$3$, \small $3$-$4$, \small $4$-$5$, \small $5$-$6$, \small $6$-$7$, \small $7$-$8$, \small $8$-$9$, \small $9$-$10$, \small $10$-$11$, \small $11$-$12$, \small 
        $12$-$13$, \small $13$-$14$, \small $14$-$15$, \small $15$-$16$, \small $16$-$17$, \small $17$-$18$, \small $18$-$19$, \small $19$-$20$, \small $\geq 20$},
        minor y tick num = 0,
        %area style,
        width=28cm,
        height=10cm,
        axis lines*=left,
        %bar width=0.2cm,
        y axis line style = {->},
        x axis line style = {->},
        tick align      = outside,
        tick pos        = left,
        title={Mean value : $\pgfmathparse{\Total/\numrows}
        \displaystyle\frac{\Total}{\numrows}=\pgfmathprintnumber{\pgfmathresult}$},
        ]
   \pgfplotsinvokeforeach{0,...,\myxmax}{%
   \edef\currentval{\csname mypile#1\endcsname}
   \pgfmathtruncatemacro{\mycur}{\currentval}
   \addplot[ybar, fill=black!20, draw=black!40, ycomb, line width=8mm, color=blue!50] coordinates {(#1,\mycur)};
   }    
  \end{axis}
 \end{tikzpicture}
\end{center}
\end{document}

введите описание изображения здесь

Или, если вам нужна средняя численность занятых,

\documentclass[a4paper, landscape]{article}


\usepackage{filecontents}
\begin{filecontents*}{commadata.dat}
8,5
13,5
6,5
8,5
10
8
5,5
2,5
5,5
7
20
12
18,5
5,5
9,5
3,5
0
7
7
5,5
10
3,5
7
14,5
7
10,5
16,5
10,5
6,5
8
14
8,5
2,5
5
9,5
8
10
9,5
9
8,5
4,5
5,5
\end{filecontents*}


%%%%%%%%%%
% Layout %
%%%%%%%%%%
\def\myHMargin{0.85cm}
\def\myVMarginTop{7mm}
\def\myVMarginBottom{7mm}
\usepackage[hmargin={\myHMargin,\myHMargin},
            vmargin={\myVMarginTop,\myVMarginBottom},
            headsep=5mm,
            footskip=\dimexpr(\baselineskip+4mm),
            includefoot,
            includehead,
            twoside]{geometry}
\pagestyle{empty}

\usepackage{xstring}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{pgfplots}
\pgfplotsset{compat=1.14}
\newcommand*{\ReadOutElement}[4]{%
    \pgfplotstablegetelem{#2}{[index]#3}\of{#1}%
    \let#4\pgfplotsretval
}


%----------------------------------------------------------------------------
\begin{document}
%----------------------------------------------------------------------------



% grid style
\pgfplotsset{grid style={dotted,gray}}


\begin{center}

%\fbox{Mean value : $\displaystyle\frac{\ ??? \ }{20}$}

 \begin{tikzpicture}
  \pgfplotstableread[/pgf/number format/read comma as period]{commadata.dat}\datatable
  \pgfplotstablegetrowsof{\datatable}
  \pgfmathtruncatemacro{\numrows}{\pgfplotsretval}
  \pgfplotstablegetcolsof{\datatable}
  \pgfmathtruncatemacro{\numcols}{\pgfplotsretval}

  \edef\myxmax{20}
  \foreach \X in {0,...,\myxmax}
  {\expandafter\xdef\csname mypile\X\endcsname{0}}
  \edef\Total{0}
  \foreach \nY in {1,...,\numrows}
  {\ReadOutElement{\datatable}{\the\numexpr\nY-1}{0}{\Current}%
   \StrSubstitute{\Current}{,}{.}[\mytemp]
   \pgfmathtruncatemacro{\myx}{\mytemp}%
   \pgfmathsetmacro{\Total}{\Total+\myx}
   \xdef\Total{\Total}
   \edef\currentval{\csname mypile\myx\endcsname}
   \pgfmathtruncatemacro{\mycur}{\currentval+1}
   \expandafter\xdef\csname mypile\myx\endcsname{\mycur}
  }
  \begin{axis}[ymajorgrids,
        ymin=0,% ymax=6.2,
        xmin=-1,xmax=21,
        %ytick={0,2,...,6},
        xtick={0,1,...,20},
        xticklabels={\small $0$-$1$, \small $1$-$2$, \small $2$-$3$, \small $3$-$4$, \small $4$-$5$, \small $5$-$6$, \small $6$-$7$, \small $7$-$8$, \small $8$-$9$, \small $9$-$10$, \small $10$-$11$, \small $11$-$12$, \small 
        $12$-$13$, \small $13$-$14$, \small $14$-$15$, \small $15$-$16$, \small $16$-$17$, \small $17$-$18$, \small $18$-$19$, \small $19$-$20$, \small $\geq 20$},
        minor y tick num = 0,
        %area style,
        width=28cm,
        height=10cm,
        axis lines*=left,
        %bar width=0.2cm,
        y axis line style = {->},
        x axis line style = {->},
        tick align      = outside,
        tick pos        = left,
%       title={Mean value : $\pgfmathparse{\Total/\numrows}
%       \displaystyle\frac{\Total}{\numrows}=\pgfmathprintnumber{\pgfmathresult}$},
        ]
   \pgfmathsetmacro{\Occ}{0}        
   \pgfplotsinvokeforeach{0,...,\myxmax}{%
   \edef\currentval{\csname mypile#1\endcsname}
   \pgfmathtruncatemacro{\mycur}{\currentval}
   \pgfmathtruncatemacro{\Occ}{\Occ+\currentval}
   \xdef\Occ{\Occ}
   \addplot[ybar, fill=black!20, draw=black!40, ycomb, line width=8mm, color=blue!50] coordinates {(#1,\mycur)};
   }    
  \end{axis}
  \node[draw,above] at (current axis.north) {Mean value :
      $\displaystyle\frac{\Occ}{20}$};
 \end{tikzpicture}
\end{center}
\end{document}

введите описание изображения здесь

решение2

Я бы сделал по-другому.

\begin{filecontents*}{\jobname.dat}
8,5
13,5
6,5
8,5
10
8
5,5
2,5
5,5
7
20
12
18,5
5,5
9,5
3,5
0
7
7
5,5
10
3,5
7
14,5
7
10,5
16,5
10,5
6,5
8
14
8,5
2,5
5
9,5
8
10
9,5
9
8,5
4,5
5,5
\end{filecontents*}

\documentclass[varwidth=40cm,border=4]{standalone}

\usepackage{xparse}

\usepackage{pgfplots}
\pgfplotsset{compat=1.14}
\pgfplotsset{grid style={dotted,gray}}

\ExplSyntaxOn

\NewDocumentCommand{\readmarks}{mm}
 {% #1 = file name, #2 = upper limit
  \colas_readmarks:nn { #1 } { #2 }
 }
\NewExpandableDocumentCommand{\getmarks}{m}
 {
  0\prop_item:Nn \l_colas_readmarks_prop { #1 }
 }
\NewExpandableDocumentCommand{\getaverage}{m}
 {
  \fp_eval:n
   {
    (0 \int_step_function:nN { #1 } \__colas_readmarks_add:n )/(#1)
   }
 }

\cs_new:Nn \__colas_readmarks_add:n
 {
  +0\prop_item:Nn \l_colas_readmarks_prop { #1 }
 }

\ior_new:N \g__colas_readmarks_stream
\prop_new:N \l_colas_readmarks_prop
\tl_new:N \l__colas_readmarks_item_tl

\cs_generate_variant:Nn \prop_put:Nnn { Nxx }
\cs_generate_variant:Nn \prop_item:Nn { Ne }

\cs_new_protected:Nn \colas_readmarks:nn
 {
  \prop_clear:N \l_colas_readmarks_prop
  \ior_open:Nn \g__colas_readmarks_stream { #1 }
  \ior_map_inline:Nn \g__colas_readmarks_stream 
   {
    \__colas_readmarks_item:nn { #2 } { ##1 }
   }
 }
\cs_new_protected:Nn \__colas_readmarks_item:nn
 {% #1 = upper limit, #2 = item
  \tl_set:Nn \l__colas_readmarks_item_tl { #2 }
  \tl_replace_once:Nnn \l__colas_readmarks_item_tl { , } { . }
  \prop_put:Nxx \l_colas_readmarks_prop
   {
    \fp_eval:n { \l__colas_readmarks_item_tl < #1 ? floor(\l__colas_readmarks_item_tl) : 20 }
   }
   {
    \int_eval:n
     {
      1 + 
      0\prop_item:Ne \l_colas_readmarks_prop
       {
        \fp_eval:n { \l__colas_readmarks_item_tl < #1 ? floor(\l__colas_readmarks_item_tl) : 20 }
       }
     }
   }
 }

\ExplSyntaxOff

\begin{document}

\readmarks{\jobname.dat}{20}

\centering

\fbox{Mean value: $\getaverage{20}$}

\begin{tikzpicture}

\begin{axis}[
  ymajorgrids,
  ymin=0,
%  ymax=6.2,
  xmin=-1,
%  ytick={0,2,...,6},
  xtick={0,1,...,20},
  xticklabels={
    \small $0$-$1$, \small $1$-$2$, \small $2$-$3$, \small $3$-$4$,
    \small $4$-$5$, \small $5$-$6$, \small $6$-$7$, \small $7$-$8$,
    \small $8$-$9$, \small $9$-$10$, \small $10$-$11$, \small $11$-$12$,
    \small $12$-$13$, \small $13$-$14$, \small $14$-$15$, \small $15$-$16$,
    \small $16$-$17$, \small $17$-$18$, \small $18$-$19$, \small $19$-$20$,
    \small $\geq 20$
  },
  minor y tick num = 0,
%   area style,
   width=28cm,
   height=10cm,
   axis lines*=left,
%   bar width=0.2cm,
   y axis line style = {->},
   x axis line style = {->},
   tick align      = outside,
   tick pos        = left
]
\pgfplotsinvokeforeach{0,...,20}{%
  \addplot[
    ybar,
    fill=black!20,
    draw=black!40,
    ycomb,
    line width=8mm,
    color=blue!50
  ] coordinates {(#1,\getmarks{#1})};
}    
\end{axis}
\end{tikzpicture}

\end{document}

Файл считывается и заполняется список свойств. Затем мы можем извлечь значения гораздо более простым способом.

введите описание изображения здесь

решение3

Не ясно, нужна ли вам средняя частота или просто среднее значение переменной x. Для второго случая:

мве

\documentclass[a4paper]{article}
\begin{document}
<<data,echo=F>>=
df <- read.csv(file="commadata.dat",head=F, dec=",", sep=";")
@

The mean is \(\frac{\Sexpr{sum(df$V1)}}{\Sexpr{length(df$V1)}}=
\Sexpr{sum(df$V1)/length(df$V1)}\)

\bigskip

<<histogran,echo=F,dev="tikz">>=
x <- round(mean(df$V1),2)
hist(df$V1, breaks=21,col="tan1",  xaxp  = c(0, 20, 20), ylim=c(0,8),
     main="", xlab="",ylab="")
arrows(x,7.8,x,0, length=0.15, col =4, code=1,lwd=2)
text(x,8,paste("$\\overline{\\mbox{x}}=$",x))
@

\end{document}

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