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%TCIDATA{<META NAME="Title" CONTENT="Statistics">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Feb 13 16:48:17 1997}
%TCIDATA{Language=American English}
%TCIDATA{CSTFile=MathHelp.cst}
%TCIDATA{<LINK REL="author" HREF="DM0-1.tex">}
%TCIDATA{<LINK REL="first" HREF="DM11-1.tex">}
%TCIDATA{<LINK REL="contents" HREF="DM0-0.tex">}
%TCIDATA{<LINK REL="copyright" HREF="DM0-2.tex">}
%TCIDATA{<LINK REL="end" HREF="DM11-9.tex">}
%TCIDATA{<LINK REL="index" HREF="DMIndex.tex">}
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\input{tcilatex}
\begin{document}


\section{Statistics\label{Statistics}}

\textsl{Scientific Notebook} supports a number of the standard statistical
distribution functions and densities, including a facility for getting
random samples from different families of distributions. It can also perform
statistical operations on data.

\subsection{\ Menu Items}

The items \textsf{Mean}, \textsf{Median}, \textsf{Mode}, \textsf{Moment}, 
\textsf{Quantile}, \textsf{Mean Deviation}, \textsf{Standard Deviation}, and 
\textsf{Variance} on the \textsf{Statistics} submenu take a single argument
that can be presented as a list of data or as a matrix. The result of an
operation is a number, or, in the case of a matrix, a number for each column.

The items \textsf{Correlation}, \textsf{Covariance}, and \textsf{Fit Curve
to Data} on the \textsf{Statistics} submenu take a single argument that must
be a matrix. For the curve-fitting commands, the columns must be labeled
with variable names. The menu item \textsf{Random Numbers} on the \textsf{%
Statistics} submenu allows you to get random samples from families of
distributions listed in the dialog box that appears when you choose \textsf{%
Random Numbers}.

\subsection{\ Lists and Matrices\label{Lists of data} \label%
{Matrices, reshape}}

\textsl{Scientific Notebook} stores data in lists 
\index{List of data@List of data}\label{List of data}or in matrices. Numbers
in a list should be separated by commas, with the numbers and commas both in
mathematics mode. Lists can be plain or enclosed in brackets. A list of data
is also referred to as a \emph{set} of data 
\index{Set of data@Set of data}\label{Set of data}. A list (not enclosed by
brackets) can be 
\index{Matrices@Matrices!reshape@reshape} 
\index{Reshape@Reshape}\label{Reshape}reshapedinto a matrix.

\begin{quote}
$\blacktriangleright $ To reshape a list or set of data into a matrix
\end{quote}

\begin{enumerate}
\item[1.]  If the list is in text, select the list and click 
\FRAME{itbpF}{0.3009in}{0.3009in}{0.0701in}{}{}{text.wmf}{\special{language
"Scientific Word";type "GRAPHIC";display "PICT";valid_file "F";width
0.3009in;height 0.3009in;depth 0.0701in;original-width
16.0625pt;original-height 16.0625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'Text.wmf';file-properties "XNPEU";}} to change
it to mathematics.

\item  Place the insertion point in the list or set.

\item  From the \textsf{Matrices} submenu, choose \textsf{Reshape.}

\item  In the dialog box that appears, enter the \textsf{Number of Columns}.

\item  Choose \textsf{OK}.

\item  Select the matrix with the mouse and click \FRAME{itbpF}{0.3009in}{%
0.3009in}{0.0701in}{}{}{brackets.wmf}{\special{language "Scientific
Word";type "GRAPHIC";display "PICT";valid_file "F";width 0.3009in;height
0.3009in;depth 0.0701in;original-width 24.0625pt;original-height
23.3125pt;cropleft "0";croptop "1";cropright "1";cropbottom "0";filename
'Brackets.wmf';file-properties "XNPEU";}}.
\end{enumerate}

\begin{quote}
$\blacktriangleright $ \textsf{Matrices + Reshape}
\end{quote}

$2,4,7,15,-8,0,-10$, (\textsf{Number of Columns}: 4) $\left[ 
\begin{array}{cccc}
2 & 4 & 7 & 15 \\ 
-8 & 0 & -10 & 
\end{array}
\right] $

$1,3.1,2,9.6,3,10.5,4,6.8,5,2.9,6,2.2$, (\textsf{Number of Columns}: 2) $%
\left[ 
\begin{array}{cc}
1 & 3.1 \\ 
2 & 9.6 \\ 
3 & 10.5 \\ 
4 & 6.8 \\ 
5 & 2.9 \\ 
6 & 2.2
\end{array}
\right] $

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Rectangular}
\end{quote}

\begin{center}
$\left[ 
\begin{array}{cc}
1 & 3.1 \\ 
2 & 9.6 \\ 
3 & 10.5 \\ 
4 & 6.8 \\ 
5 & 2.9 \\ 
6 & 2.2
\end{array}
\right] \qquad $\FRAME{itbpF}{3in}{2.0003in}{0.8752in}{}{}{}{%
\special{language "Scientific Word";type "MAPLEPLOT";width 3in;height
2.0003in;depth 0.8752in;display "PICT";plot-snapshots TRUE;function
\TEXUX{$\left[
\MATRIX{2,6}{c}\VR{,,c,,,}{,,c,,,}{,,,,,}\HR{,,,,,,}\CELL{1}\CELL{3.1}%
\CELL{2}\CELL{9.6}\CELL{3}\CELL{10.5}\CELL{4}\CELL{6.8}\CELL{5}\CELL{2.9}%
\CELL{6}\CELL{2.2}\right] $};linecolor "black";linestyle 1;linethickness
1;pointstyle "circle";pointplot TRUE;function \TEXUX{$\left[
\MATRIX{2,6}{c}\VR{,,c,,,}{,,c,,,}{,,,,,}\HR{,,,,,,}\CELL{1}\CELL{3.1}%
\CELL{2}\CELL{9.6}\CELL{3}\CELL{10.5}\CELL{4}\CELL{6.8}\CELL{5}\CELL{2.9}%
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1;pointstyle "point";xmin "0";xmax "7";xviewmin "0";xviewmax "7";yviewmin
"2.034";yviewmax "10.67";rangeset"X";phi 45;theta 45;plottype 4;numpoints
49;axesstyle "normal";xis \TEXUX{x};var1name \TEXUX{$x$};}}
\end{center}

For this plot, the matrix of points was used for two items. \textsf{Item 1}
is a \textsf{Point Plot} with \textsf{Point Symbol} set to \textsf{Circle}. 
\textsf{Item 2} has \textsf{Line Style} set to \textsf{Dots}. and \textsf{%
Line Color} set to \textsf{Green}.

\subsection{Related topics}

\begin{itemize}
\item  \hyperref{Menu Items, Lists, and Matrices}{}{}{DM11-1.tex#Statistics}

\item  \hyperref{Measures of Central Tendency}{}{}{DM11-2.tex#Statistics,
mean}

\item  \hyperref{Measures of Dispersion}{}{}{DM11-3.tex#Mean deviation}

\item  \hyperref{Distributions and Densities}{}{}{DM11-4.tex#Distribution}

\item  \hyperref{Families of Continuous Distributions}{}{}{%
DM11-5.tex#Continuous distributions}

\item  \hyperref{Families of Discrete Distributions}{}{}{DM11-6.tex#Discrete
distributions}

\item  \hyperref{Random Numbers}{}{}{DM11-7.tex#Statistics, random numbers}

\item  \hyperref{Curve Fitting}{}{}{DM11-8.tex#Curve fitting}

\item  \hyperref{Exercises and Solutions}{}{}{DM11-9.tex#Exercises}
\end{itemize}

\rule{0.67in}{0.01in}

\hyperref{\FRAME{itbpF}{0.5275in}{0.3399in}{0.0519in}{}{}{index.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid-file
"F";width 0.5275in;height 0.3399in;depth 0.0519in;original-width
36.875pt;original-height 22.5625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'index.wmf';file-properties "XNPEU";}}}{}{}{%
DMIndex.tex#Math Index}\quad {\small Index entries: \hyperref{Data}{}{}{%
DMIndex.tex#Data}, \hyperref{Matrices}{}{}{DMIndex.tex#Matrices}, \hyperref{%
Reshape}{}{}{DM8-1.tex#Reshaping}, \hyperref{Statistics}{}{}{%
DMIndex.tex#Statistics}}

\end{document}
