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.
