Let's analyze the given tables step by step.
### Understanding Table A
Table A: Garden-Type Frequencies by Column
This table shows the conditional relative frequencies by column:
\begin{tabular}{|c|c|c|c|}
\hline
& \begin{tabular}{l}
Vegetable \\
Garden
\end{tabular} & \begin{tabular}{l}
No Vegetable \\
Garden
\end{tabular} & Total \\
\hline
\begin{tabular}{l}
Flower \\
Garden
\end{tabular} & 0.28 & 0.22 & 0.25 \\
\hline
\begin{tabular}{l}
No Flower \\
Garden
\end{tabular} & 0.72 & 0.78 & 0.75 \\
\hline
Total & 1.0 & 1.0 & 1.0 \\
\hline
\end{tabular}
- The first column represents people who have a Vegetable Garden.
- Out of these, 28% also have a Flower Garden (0.28).
- 72% do not have a Flower Garden (0.72).
- Total = 100% = 1.0.
- The second column represents people who do not have a Vegetable Garden.
- Out of these, 22% have a Flower Garden (0.22).
- 78% do not have a Flower Garden (0.78).
- Total = 100% = 1.0.
### Understanding Table B
Table B: Garden-Type Frequencies by Row
This table shows the conditional relative frequencies by row:
\begin{tabular}{|c|c|c|c|}
\hline
& \begin{tabular}{l}
Vegetable \\
Garden
\end{tabular} & \begin{tabular}{l}
No Vegetable \\
Garden
\end{tabular} & Total \\
\hline
\begin{tabular}{l}
Flower \\
Garden
\end{tabular} & 0.56 & 0.44 & 1.0 \\
\hline
\end{tabular}
- The first row represents people who have a Flower Garden.
- Out of these, 56% also have a Vegetable Garden (0.56).
- 44% do not have a Vegetable Garden (0.44).
- Total = 100% = 1.0.
### Explanation
1. Flower Garden:
- From Table A, among people with vegetable gardens, 28% have flower gardens.
- Among people without vegetable gardens, 22% have flower gardens.
- From Table B, among people with flower gardens, 56% have vegetable gardens.
2. No Flower Garden:
- From Table A, among people with vegetable gardens, 72% do not have flower gardens.
- Among people without vegetable gardens, 78% do not have flower gardens.
3. Overall Distribution:
- The total percentages add up to 100% horizontally in each table, indicating a thorough classification.
### Conditional Probabilities:
The tables give us insight into conditional probabilities. For example:
- The probability of having a Flower Garden given that someone has a Vegetable Garden = 0.28.
- The probability of having a Vegetable Garden given that someone has a Flower Garden = 0.56.
Ultimately, these tables provide valuable data about the types of gardens people maintain in the community and how these preferences are related.
