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.