Questions: Constructing a frequency distribution and a frequency polygon Here are the hottest recorded temperatures (in °F) for each of sixteen cities throughout North America. Temperatures (in °) 94 96 103 112 102 101 105 105 93 97 110 94 104 99 106 99 (a) Complete the grouped frequency distribution for the data. (Note that the class width is 4.) Temperatures (in °F) Frequency 92.5 to 96.5 96.5 to 100.5 100.5 to 104.5 104.5 to 108.5

Constructing a frequency distribution and a frequency polygon Here are the hottest recorded temperatures (in °F) for each of sixteen cities throughout North America. Temperatures (in °) 94 96 103 112 102 101 105 105 93 97 110 94 104 99 106 99

(a) Complete the grouped frequency distribution for the data. (Note that the class width is 4.) Temperatures (in °F) Frequency 92.5 to 96.5 96.5 to 100.5 100.5 to 104.5 104.5 to 108.5

Transcript text: Constructing a frequency distribution and a frequency polygon Here are the hottest recorded temperatures (in ${ }^{\circ} \mathrm{F}$ ) for each of sixteen cities throughout North America. \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline \multicolumn{8}{|c|}{\begin{tabular}{c} Temperatures \\ (in ${ }^{\circ}$ ) \end{tabular}} \\ \hline 94 & 96 & 103 & 112 & 102 & 101 & 105 & 105 \\ \hline 93 & 97 & 110 & 94 & 104 & 99 & 106 & 99 \\ \hline \end{tabular} (a) Complete the grouped frequency distribution for the data. (Note that the class width is 4 .) \begin{tabular}{|cc|} \hline \begin{tabular}{c} Temperatures \\ (in ${ }^{\circ} \mathrm{F}$ ) \end{tabular} & Frequency \\ \hline 92.5 to 96.5 & $\square$ \\ 96.5 to 100.5 & $\square$ \\ 100.5 to 104.5 & $\square$ \\ 104.5 to 108.5 & $\square$ \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Define the Class Intervals

The class intervals for the grouped frequency distribution are defined as follows:

$ 92.5 $ to $ 96.5 $
$ 96.5 $ to $ 100.5 $
$ 100.5 $ to $ 104.5 $
$ 104.5 $ to $ 108.5 $

Step 2: Count Frequencies for Each Interval

Next, we count the number of temperatures that fall within each class interval:

For the interval $ 92.5 $ to $ 96.5 $, the temperatures $ 94, 96, 93, 94 $ fall within this range, resulting in a frequency of $ 4 $.
For the interval $ 96.5 $ to $ 100.5 $, the temperatures $ 97, 99 $ fall within this range, resulting in a frequency of $ 3 $.
For the interval $ 100.5 $ to $ 104.5 $, the temperatures $ 103, 102, 101, 104 $ fall within this range, resulting in a frequency of $ 4 $.
For the interval $ 104.5 $ to $ 108.5 $, the temperatures $ 105, 105, 106 $ fall within this range, resulting in a frequency of $ 3 $.

Step 3: Compile the Frequency Distribution

The compiled frequency distribution based on the counts from the previous step is as follows: \[ \begin{array}{|c|c|} \hline \text{Temperatures (in }^{\circ} \mathrm{F}\text{)} & \text{Frequency} \\ \hline 92.5 \text{ to } 96.5 & 4 \\ 96.5 \text{ to } 100.5 & 3 \\ 100.5 \text{ to } 104.5 & 4 \\ 104.5 \text{ to } 108.5 & 3 \\ \hline \end{array} \]

Final Answer

\[ \begin{array}{|c|c|} \hline \text{Temperatures (in }^{\circ} \mathrm{F}\text{)} & \text{Frequency} \\ \hline 92.5 \text{ to } 96.5 & 4 \\ 96.5 \text{ to } 100.5 & 3 \\ 100.5 \text{ to } 104.5 & 4 \\ 104.5 \text{ to } 108.5 & 3 \\ \hline \end{array} \]

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