Given the table of college enrollment data:
\begin{tabular}{|l|l|r|r|}
\hline Age Group & Male & Female & Marginal Total \\
\hline [tex]$1 8 - 2 4$[/tex] & 5,640 & 6,432 & 12,072 \\
\hline [tex]$2 5 - 3 4$[/tex] & 1,843 & 2,450 & 4,293 \\
\hline [tex]$3 5 +$[/tex] & 1,069 & 2,124 & 3,193 \\
\hline Total & 8,552 & 11,006 & 19,558 \\
\hline
\end{tabular}
First, we need to understand what the marginal total 4,293 represents. The marginal total 4,293 is the total number of students in the [tex]$25 - 34$[/tex] age group (both male and female combined).
Therefore, the marginal total 4,293 is the total number of students in the 25 - 34 age group.
Next, we need to calculate the relative frequency of females in the [tex]$35+$[/tex] age group compared with the total number of students, and express this as a percentage.
1. The number of females in the [tex]$35+$[/tex] age group is 2,124.
2. The total number of students surveyed is 19,558.
To find the relative frequency of females in the [tex]$35+$[/tex] age group:
[tex]\[ \text{Relative frequency} = \frac{\text{Number of females in the } 35+ \text{ age group}}{\text{Total number of students}} \times 100\% \][/tex]
[tex]\[ \text{Relative frequency} = \frac{2,124}{19,558} \times 100\% \][/tex]
Calculating this:
[tex]\[ \frac{2,124}{19,558} \approx 0.1086 \][/tex]
[tex]\[ 0.1086 \times 100\% = 10.86\% \][/tex]
Therefore, the relative frequency of females in the [tex]$35+$[/tex] age group, expressed as a percentage, is 10.86%.
