Answer :
To find the relative frequencies by column, we need to calculate the fraction each cell contributes to its respective column total. Let's break down the calculations step-by-step.
First, we start with the column for kids:
1. Column Total for Kids: The total number of kids surveyed is given as [tex]\(20\)[/tex].
2. Calculating Relative Frequency for Kids preferring Beach:
[tex]\[ \text{Relative Frequency} = \frac{\text{Number of Kids preferring Beach}}{\text{Total Kids}} = \frac{14}{20} = 0.7 \][/tex]
3. Calculating Relative Frequency for Kids preferring Pool:
[tex]\[ \text{Relative Frequency} = \frac{\text{Number of Kids preferring Pool}}{\text{Total Kids}} = \frac{6}{20} = 0.3 \][/tex]
Next, we move to the column for parents:
1. Column Total for Parents: The total number of parents surveyed is also given as [tex]\(20\)[/tex].
2. Calculating Relative Frequency for Parents preferring Beach:
[tex]\[ \text{Relative Frequency} = \frac{\text{Number of Parents preferring Beach}}{\text{Total Parents}} = \frac{8}{20} = 0.4 \][/tex]
3. Calculating Relative Frequency for Parents preferring Pool:
[tex]\[ \text{Relative Frequency} = \frac{\text{Number of Parents preferring Pool}}{\text{Total Parents}} = \frac{12}{20} = 0.6 \][/tex]
Now, let's place these relative frequencies back into the two-way table:
[tex]\[ \begin{tabular}{|l|c|c|c|} \cline { 2 - 4 } \multicolumn{1}{c|}{} & Kids & Parents & Total \\ \hline Beach & 0.7 & 0.4 & \\ \hline Pool & 0.3 & 0.6 & \\ \hline Total & 1.0 & 1.0 & \\ \hline \end{tabular} \][/tex]
By following these steps, you have successfully calculated the relative frequencies by column for the given data set.
First, we start with the column for kids:
1. Column Total for Kids: The total number of kids surveyed is given as [tex]\(20\)[/tex].
2. Calculating Relative Frequency for Kids preferring Beach:
[tex]\[ \text{Relative Frequency} = \frac{\text{Number of Kids preferring Beach}}{\text{Total Kids}} = \frac{14}{20} = 0.7 \][/tex]
3. Calculating Relative Frequency for Kids preferring Pool:
[tex]\[ \text{Relative Frequency} = \frac{\text{Number of Kids preferring Pool}}{\text{Total Kids}} = \frac{6}{20} = 0.3 \][/tex]
Next, we move to the column for parents:
1. Column Total for Parents: The total number of parents surveyed is also given as [tex]\(20\)[/tex].
2. Calculating Relative Frequency for Parents preferring Beach:
[tex]\[ \text{Relative Frequency} = \frac{\text{Number of Parents preferring Beach}}{\text{Total Parents}} = \frac{8}{20} = 0.4 \][/tex]
3. Calculating Relative Frequency for Parents preferring Pool:
[tex]\[ \text{Relative Frequency} = \frac{\text{Number of Parents preferring Pool}}{\text{Total Parents}} = \frac{12}{20} = 0.6 \][/tex]
Now, let's place these relative frequencies back into the two-way table:
[tex]\[ \begin{tabular}{|l|c|c|c|} \cline { 2 - 4 } \multicolumn{1}{c|}{} & Kids & Parents & Total \\ \hline Beach & 0.7 & 0.4 & \\ \hline Pool & 0.3 & 0.6 & \\ \hline Total & 1.0 & 1.0 & \\ \hline \end{tabular} \][/tex]
By following these steps, you have successfully calculated the relative frequencies by column for the given data set.
