To determine which of the provided tables could be a conditional relative frequency table, we need to examine the structure and totals presented in each table.
A conditional relative frequency table shows the relative frequencies of a certain condition and sums to 1.0 for the total column of each subcategory (typically denoted by rows).
### Table 1:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
& A & B & \text{Total} \\
\hline
C & 0.25 & 0.25 & 0.50 \\
\hline
D & 0.25 & 0.25 & 0.50 \\
\hline
\text{Total} & 0.50 & 0.50 & 1.0 \\
\hline
\end{array}
\][/tex]
- Sum of C row: [tex]\(0.25 + 0.25 = 0.50\)[/tex]
- Sum of D row: [tex]\(0.25 + 0.25 = 0.50\)[/tex]
- Sum of Total column: [tex]\(0.50 + 0.50 = 1.0\)[/tex]
The totals do not sum to 1 within individual rows for conditional relative frequencies as typically expected.
### Table 2:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
& A & B & \text{Total} \\
\hline
C & 0.25 & 0.75 & 1.0 \\
\hline
D & 0.35 & 0.65 & 1.0 \\
\hline
\text{Total} & 0.30 & 0.70 & 1.0 \\
\hline
\end{array}
\][/tex]
- Sum of C row: [tex]\(0.25 + 0.75 = 1.0\)[/tex]
- Sum of D row: [tex]\(0.35 + 0.65 = 1.0\)[/tex]
- Sum of Total column: [tex]\(0.30 + 0.70 = 1.0\)[/tex]
The totals sum to 1 within individual rows, which fits the definition of a conditional relative frequency table.
### Table 3:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
& A & B & \text{Total} \\
\hline
C & 0.75 & 0.25 & 0.50 \\
\hline
\end{array}
\][/tex]
- Sum of C row: [tex]\(0.75 + 0.25 = 1.0\)[/tex]
- No other data to validate.
In conclusion, based on the examination:
- Table 2 is the conditional relative frequency table because the relative frequencies in each row sum to 1.
