\setcounter{ExampleCounter}{1}
So far in this chapter, we've summarized data visually.  Now we come to summarizing data numerically.  We'll start by summarizing where the data is centered, using three measures:
\begin{enumerate}
\item \text{}
\vspace{0.2in}

\item \text{}
\vspace{0.2in}

\item \text{}
\vspace{0.2in}

\end{enumerate}

\begin{proc}{Mean, Median, and Mode}
\paragraph{Mean or Average:} \text{}
\vspace{0.75in}

For a sample of size $n$, 
\vspace{0.5in}

For a population of size $N$, 
\vspace{0.5in}

\paragraph{Median:} \text{}
\vspace{0.75in}

The median is at position 
\vspace{0.5in}

\paragraph{Mode:} \text{}
\vspace*{0.75in}

\end{proc}
\vfill
\pagebreak

The easiest way to find the mean and median is by using your calculator:
\begin{enumerate}
\item Enter the data by pressing \includegraphics[height=0.3in]{CalcStatButton} \includegraphics[height=0.15in]{CalcEdit}
\item Press \includegraphics[height=0.3in]{CalcStatButton} again and scroll over to the \verb|CALC| menu.
\begin{center}
\includegraphics[width=3in]{Calc3Sec1_2}
\end{center}
\item Press \includegraphics[height=0.3in]{CalcEnterButton} to select \verb|1-Var Stats|
\item Scroll down to \verb|Calculate| on the menu and press \includegraphics[height=0.3in]{CalcEnterButton}
\item Scroll through the resulting list to find $\overline{x}$ and \verb|Med|.
\begin{center}
\includegraphics[width=3in]{Calc1VarStats}
\end{center}
\end{enumerate}
\vfill
\pagebreak

\subsection{From a Frequency Table}
\begin{example}{Mean and Median}
Calculate the mean and median of the data set summarized by the following frequency table.
\begin{center}
\begin{tabular}{c c}
Score & Frequency\\
\hline
\\
68 & 3\\
71 & 2\\
75 & 5\\
77 & 3\\
83 & 4\\
89 & 3
\end{tabular}
\end{center}

\paragraph{Mean} \text{}
\vspace{2.5in}

\paragraph{Median} \text{}
\vspace{2.5in}
\end{example}
\vfill
\pagebreak

This can be done using calculator as well.  Enter the data as a frequency table:
\begin{center}
\includegraphics[width=3in]{CalcMeanFreqTable}
\end{center}

Then \marginnote{On the TI-83, when you hit enter on \texttt{1-Var Stats}, you'll be taken back to the home screen with that entered.  Type in \texttt{L1, L2} by pressing \texttt{2nd} $\longrightarrow$ \texttt{1} $\longrightarrow$ \texttt{,} $\longrightarrow$ \texttt{2nd} $\longrightarrow$ \texttt{2}}when you select \verb|1-Var Stats|, enter \verb|L2| as the \verb|FreqList| (using \verb|2nd| $\longrightarrow$ \verb|2|).
\begin{center}
\includegraphics[width=3in]{CalcMeanFreqTable2}
\end{center}

\begin{example}{Mean and Median}
Find the mean, median, and mode for the data set summarized by the following frequency table, the frequency of airline no-shows.
\begin{center}
\begin{tabular}{c c}
Number of No-Shows & Frequency\\
\hline
\\
0 & 37\\
1 & 31\\
2 & 20\\
3 & 16\\
4 & 12\\
5 & 4
\end{tabular}
\end{center}

\paragraph{Mean:} \text{}
\vspace{0.1in}

\paragraph{Median:} \text{}
\vspace{0.1in}

\paragraph{Mode:} \text{}
\vspace*{0.1in}
\end{example}


