Here are the hottest recorded temperatures (in ${ }^{\circ} \mathrm{F}$ ) for each of fifteen cities throughout North America.
\begin{tabular}{|c|c|c|c|c|}
\hline \multicolumn{5}{|c|}{\begin{tabular}{c}
Temperatures \\
(in $\left.{ }^{\circ} \mathrm{F}\right)$
\end{tabular}} \\
\hline 107 & 117 & 106 & 105 & 104 \\
111 & 109 & 102 & 101 & 103 \\
111 & 98 & 100 & 111 & 113 \\
\hline
\end{tabular}
(a) Complete the grouped frequency distribution for the data. (Note that the class width is 5 .)
\begin{tabular}{|cc|}
\hline \begin{tabular}{c}
Temperatures \\
(in $^{\circ}$ F)
\end{tabular} & Frequency \\
\hline $97.5-102.5$ & $\square$ \\
$102.5-107.5$ & $\square$ \\
$107.5-112.5$ & $\square$ \\
$112.5-117.5$ & $\square$ \\
\hline
\end{tabular}
(b) Construct a histogram for the data.

Step 1 ：Given the recorded temperatures for fifteen cities throughout North America, we are asked to complete the grouped frequency distribution for the data and construct a histogram. The temperatures are as follows: 107, 117, 106, 105, 104, 111, 109, 102, 101, 103, 111, 98, 100, 111, 113.

Step 2 ：We define the ranges for the grouped frequency distribution as follows: 97.5-102.5, 102.5-107.5, 107.5-112.5, 112.5-117.5.

Step 3 ：We then iterate over the temperatures and check which range each temperature falls into. We increment the corresponding count for each range.

Step 4 ：By doing this, we find the frequencies of temperatures in each range to be: 4, 5, 4, 2.

Step 5 ：Thus, the completed grouped frequency distribution is as follows: \n\n\begin{tabular}{|cc|}\n\hline \begin{tabular}{c} \nTemperatures \\(in $^{\circ}$ F)\n\end{tabular} & Frequency \\\n\hline $97.5-102.5$ & $4$ \\\n$102.5-107.5$ & $5$ \\\n$107.5-112.5$ & $4$ \\\n$112.5-117.5$ & $2$ \\\n\hline\n\end{tabular}

Step 6 ：Finally, we can construct a histogram for the data using these frequencies.