How to create a table automatically for a homework in statistics?

Question

I want to create a long table containing some statistical data, such as the sample, the average, and the variance, etc. I am using the pgf package and its various extensions to do this.

Here is a silly MWE:

\documentclass{article}
\usepackage{pgf}
\usepackage{tikz}
\usepgflibrary{fpu}
\pgfmathsetseed{\number\pdfrandomseed}
\begin{document}
\xdef\Sum{0}
\xdef\Rand{0}
\xdef\Avg{0}
\xdef\Var{0}
\xdef\Sq{0}
%\begin{table}[h]
%\begin{tabular}{|c|c|c|c|c|c|}
%\hline
%Trial & Rand & Sum & Sum-of-squares & Average & Variance\\
%\hline\hline
%\noindent Trial Rand Sum Sum-of-squares Average Variance\\
\noindent\foreach \i in {1 ,...,15} {
    %\pgfkeys{/pgf/fpu,/pgf/fpu/output format=sci}
        \pgfmathparse{random(10)}
        \xdef\Rand{\pgfmathresult}
        \pgfkeys{/pgf/fpu,/pgf/fpu/output format=sci}
        \pgfmathparse{\Sum+\Rand}
        \xdef\Sum{\pgfmathresult}
        \pgfmathparse{\Sq+\Rand*\Rand}
        \xdef\Sq{\pgfmathresult}
        \pgfmathparse{\Sum/\i}
        \xdef\Avg{\pgfmathresult}
        \pgfmathparse{\Sq/\i-\Avg*\Avg}
        \xdef\Var{\pgfmathresult}
        \noindent \i,\                             %&%
        \pgfmathparse{\Rand}\pgfmathresult,\    %&%
        \pgfmathparse{\Sum}\pgfmathresult,\      %&%
        \pgfmathparse{\Sq}\pgfmathresult,         %&%
        \pgfmathparse{\Avg}\pgfmathresult,       %&%
        \pgfmathparse{\Var}\pgfmathresult        \\
        %\hline
        }
        %\end{tabular}
%\end{table}
\end{document}

Here is an output (depending on what random numbers you get):

As you can see, the table is commented out, as I have given up on it. I want to generate a document like this with 1000 pages, and see the computed empirical average and variance.

---

Very closely related:

• How do I use the ampersand (&) inside a foreach or conditional (or other group/environment) when building tables?
• Copy table row n times
• Generate table using the foreach command from pgffor
• how to get rid of extra \hline drawn before start of longtable?

---

Note: this question has been heavily edited due to showing signs of the XY problem. I will reask problem X in a separate question later.

Answer 1

I suspected that your question How do I use the ampersand (&) inside a foreach or conditional (or other group/environment) when building tables? was of the XY type.

The usual problem in these cases is that you cannot build a table inside a \foreach statement, because table cells form groups. The strategy is to build the table body beforehand.

\documentclass{article}

\usepackage{booktabs,etoolbox}

\usepackage{pgf}
\usepackage{tikz}
\usepgflibrary{fpu}

\pgfmathsetseed{\number\pdfrandomseed}

\begin{document}

\def\Sum{0}
\def\Rand{0}
\def\Avg{0}
\def\Var{0}
\def\Sq{0}
\def\TableBody{}
\foreach \i in {1,...,15} {
  %\pgfkeys{/pgf/fpu,/pgf/fpu/output format=sci}
  \pgfmathparse{random(10)}
  \xdef\Rand{\pgfmathresult}
  \pgfkeys{/pgf/fpu,/pgf/fpu/output format=sci}
  \pgfmathparse{\Sum+\Rand}
  \xdef\Sum{\pgfmathresult}
  \pgfmathparse{\Sq+\Rand*\Rand}
  \xdef\Sq{\pgfmathresult}
  \pgfmathparse{\Sum/\i}
  \xdef\Avg{\pgfmathresult}
  \pgfmathparse{\Sq/\i-\Avg*\Avg}
  \xdef\Var{\pgfmathresult}
  \xappto\TableBody{\i & \Rand & \Sum & \Sq & \Avg & \Var \noexpand\\}
}

\begin{tabular}{ *{6}{c} }
\toprule
Trial & Rand & Sum & Sum-of-squares & Average & Variance \\
\midrule
\TableBody
\bottomrule
\end{tabular}

\end{document}

Here's what I get with longtable and 500 draws.

Answer 2

I am no expert in pgfplotstable but here is an idea to build upon.

To get the entries to align prettier, see Q131081.

(I find pgfplotstable overly complicated and it surely doesn't help that the manual repeats parts of the PGFmanual …)

Code

\documentclass{article}
\usepackage{booktabs,pgfplotstable}
\pgfmathsetseed{\number\pdfrandomseed}
\pgfplotstableset{
  duck ini/.style={columns={Trial,Rand}},
  duck table/.style={
    columns={Trial,Rand,Sum,Sq,Avg,Var},
    set column name/.list={Sq:Sum-of-squared, Avg:Average, Var:Variance},
    every head row/.append style={before row=\toprule, after row=\midrule},
    every last row/.append style={after row=\bottomrule},
    set column/.list={Avg:prec=1, Var:prec=2}},
  set column name/.style args={#1:#2}{columns/#1/.append style={column name={#2}}},
  set column/.style args={#1:#2}{columns/#1/.append style={#2}},
  set expr/.style args={#1=#2}{create on use/#1/.style={create col/expr={#2}}}}
\pgfset{number format/prec/.style={fixed, fixed zerofill, precision={#1}}}
\pgfplotstableset{set expr/.list={Trial=\pgfplotstablerow+1,Rand=int(rnd*11)}}
\newcommand*\addmyusualcolumns[1]{%
  \pgfplotstablecreatecol[expr={\pgfmathaccuma+\thisrow{Rand}}]                           {Sum} #1
  \pgfplotstablecreatecol[expr={\pgfmathaccuma+\thisrow{Rand}*\thisrow{Rand}}]            {Sq}  #1
  \pgfplotstablecreatecol[expr={\thisrow{Sum}/\thisrow{Trial}}]                           {Avg} #1
  \pgfplotstablecreatecol[expr={\thisrow{Sq}/\thisrow{Trial}-\thisrow{Avg}*\thisrow{Avg}}]{Var} #1}
\begin{document}
\pgfplotstablenew[duck ini]{15}\t
\addmyusualcolumns\t
\pgfplotstabletypeset[duck table]\t

\pgfplotstablenew[duck ini]{30}\T
\addmyusualcolumns\T
\pgfplotstabletypeset[duck table]\T
\end{document}