Here are the hottest recorded temperatures (in [tex]${ }^{\circ} F$[/tex]) for eight cities throughout North America. Complete the grouped frequency distribution for the data.

In the distribution, the frequency of a class is the number of temperatures in that class. (Note that we are using a class width of 5.)

\begin{tabular}{|c|c|c|c|}
\hline \multicolumn{4}{|c|}{Temperature (in [tex]${ }^{\circ} F$[/tex])} \\
\hline 113 & 104 & 117 & 103 \\
\hline 116 & 108 & 113 & 110 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|}
\hline Temperature (in [tex][tex]${ }^{\circ} F$[/tex][/tex]) & Frequency \\
\hline 103 to 107 & \\
\hline 108 to 112 & \\
\hline 113 to 117 & \\
\hline
\end{tabular}



Answer :

To complete the grouped frequency distribution for the hottest recorded temperatures, we'll follow these steps:

1. List Temperatures and Class Intervals:
- The recorded temperatures are: 113, 104, 117, 103, 116, 108, 113, and 110.
- The class intervals given are:
- 103 to 107
- 108 to 112
- 113 to 117

2. Count the Frequency for Each Class Interval:
- For the class interval 103 to 107:
- We need to count how many temperatures fall between 103 and 107, inclusive.
- Temperatures in this range: 104 and 103.
- So, there are 2 temperatures in this class.

- For the class interval 108 to 112:
- We need to count how many temperatures fall between 108 and 112, inclusive.
- Temperatures in this range: 108 and 110.
- So, there are 2 temperatures in this class.

- For the class interval 113 to 117:
- We need to count how many temperatures fall between 113 and 117, inclusive.
- Temperatures in this range: 113, 117, 116, and 113.
- So, there are 4 temperatures in this class.

3. Complete the Frequency Distribution Table:

[tex]\[ \begin{array}{|c|c|} \hline \begin{tabular}{l} Temperature \\ (in { }^{\circ}\text{F}) \end{tabular} & \text{Frequency} \\ \hline 103 \text{ to } 107 & 2 \\ \hline 108 \text{ to } 112 & 2 \\ \hline 113 \text{ to } 117 & 4 \\ \hline \end{array} \][/tex]

Thus, the grouped frequency distribution for the data is:
- 103 to 107: Frequency = 2
- 108 to 112: Frequency = 2
- 113 to 117: Frequency = 4