Problem

Use the frequency distribution shown below to construct an expanded frequency distribution. High Temperatures ( ${ }^{\circ} \mathrm{F}$ ) \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline Class & $18-28$ & $29-39$ & $40-50$ & $51-61$ & $62-72$ & $73-83$ & $84-94$ \\ \hline Frequency, $\mathrm{f}$ & 17 & 42 & 68 & 69 & 75 & 68 & 26 \\ \hline \end{tabular} Complete the table below. High Temperatures $\left({ }^{\circ} \mathrm{F}\right) \quad$ (Round to the nearest hundredth as needed.) \begin{tabular}{|l|c|c|c|c|} \hline Class & Frequency, $\mathrm{f}$ & Midpoint & \begin{tabular}{l} Relative \\ frequency \end{tabular} & \begin{tabular}{l} Cumulative \\ frequency \end{tabular} \\ \hline $18-28$ & 17 & 23 & 0.05 & 17 \\ \hline $29-39$ & 42 & 34 & 0.12 & 59 \\ \hline $40-50$ & 68 & 45.0 & 0.19 & 127 \\ \hline $51-61$ & 69 & 56.0 & 0.19 & 196 \\ \hline $62-72$ & 75 & 67 & 0.21 & 271 \\ $73-83$ & 68 & $\square$ & $\square$ & $\square$ \\ \hline \end{tabular}

Solution

Step 1 :The question asks to complete the table for the class 73-83. We need to find the midpoint, relative frequency, and cumulative frequency for this class.

Step 2 :The midpoint of a class is calculated as the average of the lower and upper limits of the class. In this case, the lower limit is 73 and the upper limit is 83. So, the midpoint is \((73+83)/2 = 78.0\).

Step 3 :The relative frequency of a class is the frequency of the class divided by the total frequency. The total frequency can be calculated by summing up all the frequencies given in the table. The total frequency is \(17+42+68+69+75+68 = 339\). So, the relative frequency is \(68/339 = 0.20\) (rounded to the nearest hundredth).

Step 4 :The cumulative frequency of a class is the sum of the frequencies of that class and all previous classes. In this case, we need to add the frequency of the class 73-83 to the cumulative frequency of the previous class, which is 271. So, the cumulative frequency is \(271+68 = 339\).

Step 5 :\(\boxed{\text{The midpoint for the class } 73-83 \text{ is } 78.0, \text{ the relative frequency (rounded to the nearest hundredth) is } 0.20, \text{ and the cumulative frequency is } 339. \text{ Therefore, the completed row in the table is:}}\)

Step 6 :\begin{tabular}{|l|c|c|c|c|} \hline Class & Frequency, $\mathrm{f}$ & Midpoint & \begin{tabular}{l} Relative \\ frequency \end{tabular} & \begin{tabular}{l} Cumulative \\ frequency \end{tabular} \\ \hline $73-83$ & 68 & 78.0 & 0.20 & 339 \\ \hline \end{tabular}

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Source: https://solvelyapp.com/problems/aeVBK3VpgH/

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