\setcounter{ExampleCounter}{1}
Frequency tables simply count how many times each data value occurs and list this count.

\subsection{Qualitative Data}
\begin{example}{Student Grades}
Suppose a group of students earned the following final grades:
\begin{center}
B, C, A, B, B, D, C, C, C, F, A, C, B, B, B, C, B, D
\end{center}

The frequency table for this data would look like the following.
\begin{center}
\begin{tabular}{c c c}
Grade & Frequency\\
\hline
A & 2\\
B & 7\\
C & 6\\
D & 2\\
F & 1
\end{tabular}
\end{center}

\paragraph{Relative Frequency:} The proportion of the whole group that is in each category.
\begin{center}
\begin{tabular}{c c c}
Grade & Frequency & Relative Frequency\\
\hline
& & \\
A & 2 & 2/18 = 0.11\\
& & \\
B & 7 & 0.39\\
& & \\
C & 6 & 0.33\\
& & \\
D & 2 & 0.11\\
& & \\
F & 1 & 0.06
\end{tabular}
\end{center}
\end{example}
\vfill
\pagebreak

\subsection{Quantitative Data}
\begin{example}{iPads Sold}
A store tracked how many iPads were sold each day for fifty days, and their data is below.
\begin{center}
\begin{tabular}{c c c c c c c c c c}
4 & 2 & 3 & 2 & 5 & 5 & 1 & 3 & 3 & 2\\
3 & 2 & 2 & 3 & 2 & 2 & 2 & 3 & 0 & 1\\
3 & 1 & 1 & 5 & 4 & 1 & 2 & 4 & 3 & 5\\
2 & 0 & 0 & 3 & 2 & 3 & 3 & 3 & 2 & 2\\
0 & 4 & 2 & 4 & 3 & 1 & 1 & 4 & 0 & 1
\end{tabular}
\end{center}

The frequency distribution looks like the following.
\begin{center}
\begin{tabular}{c c c}
Value & Frequency & Relative Frequency\\
\hline
0 & 5 & 0.10\\
1 & 8 & 0.16\\
2 & 14 & 0.28\\
3 & 13 & 0.26\\
4 & 6 & 0.12\\
5 & 4 & 0.08
\end{tabular}
\end{center}
\end{example}
\vspace{0.2in}

\begin{example}{Working Students}
Twenty students were asked how many hours they worked per day.  Their responses are as follows:
\begin{center}
5, \ 6,\ 3,\ 3,\ 2,\ 4,\ 7,\ 5,\ 2,\ 3,\ 5,\ 6,\ 5,\ 4,\ 4,\ 3,\ 5,\ 2,\ 5,\ 3
\end{center}

Construct a frequency table (including a relative frequency column) to organize this data.
\begin{center}
\begin{tabular}{c | c | c}
Hours Worked & Frequency & Relative Frequency\\
\hline
2 & 3 & 3/20 = 0.15\\
3 & 5 & 5/20 = 0.25\\
4 & 3 & 3/20 = 0.15\\
5 & 6 & 6/20 = 0.30\\
6 & 2 & 2/20 = 0.10\\
7 & 1 & 1/20 = 0.05\\
\end{tabular}
\end{center}
\end{example}
\vfill
\pagebreak

\subsection{Grouped Frequency Tables}
Sometimes it could be inconvenient to have a separate row for each data value.  For instance, consider the following wait times on a customer service line (measured in minutes):
\begin{center}
\begin{tabular}{c c c c c c c c c c}
0.6 & 1.2 & 1.3 & 2.5 & 2.8 & 3.2 & 3.2 & 3.5 & 3.8 & 3.9\\
3.9 & 4.4 & 4.4 & 4.6 & 4.6 & 4.6 & 4.8 & 4.9 & 5.1 & 5.2\\
5.4 & 5.5 & 5.8 & 6.1 & 6.4 & 6.9 & 7.0 & 8.0 & 8.1 & 8.1\\
8.3 & 8.7 & 9.0 & 9.3 & 9.3 & 9.5 & 9.5 & 9.7 & 9.8 & 9.9\\
10.2 & 10.5 & 10.9 & 12.2 & 12.5 & 13.1 & 13.3 & 13.6 & 14.4 & 17.4
\end{tabular}
\end{center}

If we had a separate category for each time, there would be a bunch of categories with a frequency of 1 or 2.  Instead, we'll construct a \textbf{grouped frequency table}:
\begin{itemize}
\item Separate the data into \emph{bins}, or classes
\item All classes must have the same width
\item The classes cannot overlap; for example, one class cannot be 0 to 3 minutes if another is 3 to 6 minutes
\item There must be enough classes to cover the data
\item Avoid empty classes and open-ended classes
\end{itemize}
\vfill
\pagebreak

\begin{example}{Customer Service Wait Times}
Construct a grouped frequency table for the data above, using a class width of 3 minutes.

\begin{center}
\begin{tabular}{c c c}
Number of Minutes & Frequency & Relative Frequency\\
\hline
$0 \leq t < 3$ & 5 & 0.10\\
$3 \leq t < 6$ & 18 & 0.36\\
$6 \leq t < 9$ & 9 & 0.18\\
$9 \leq t < 12$ & 11 & 0.22\\
$12 \leq t < 15$ & 6 & 0.12\\
$15 \leq t < 18$ & 1 & 0.02
\end{tabular}
\end{center}
\end{example}



