To solve the given problem, we need to handle two separate parts:
1. Determine what the marginal total of 4,293 represents.
2. Calculate the relative frequency of females in the 35+ age group as a percentage of the total number of students.
### Part 1: Marginal Total of 4,293
Looking at the table, the marginal total of 4,293 appears in the row corresponding to the 25-34 age group. Marginal totals represent the sum of all categories in a particular row or column. So, the marginal total of 4,293 is the total number of students (both male and female) in the 25-34 age group.
### Answer Part 1: The marginal total 4,293 is the total number of students in the 25-34 age group.
### Part 2: Relative Frequency of Females in the 35+ Age Group
We need to calculate the relative frequency of females in the 35+ age group as a percentage of the total number of students.
We'll follow these steps:
1. Identify the number of females in the 35+ age group, which is 2,124.
2. Identify the total number of students, which is 19,558.
3. Calculate the relative frequency using the formula:
[tex]\[
\text{Relative Frequency} = \left( \frac{\text{Number of Females in the 35+ Age Group}}{\text{Total Number of Students}} \right) \times 100
\][/tex]
### Calculation
[tex]\[
\text{Relative Frequency} = \left( \frac{2,124}{19,558} \right) \times 100
\][/tex]
First, divide 2,124 by 19,558:
[tex]\[
\frac{2,124}{19,558} \approx 0.1086
\][/tex]
Then, multiply by 100 to convert to a percentage:
[tex]\[
0.1086 \times 100 \approx 10.86\%
\][/tex]
### Answer Part 2: The relative frequency of females in the 35+ age group compared with the total number of students, expressed as a percentage, is 10.86%.
### Summary
- The marginal total 4,293 is the total number of students in the 25-34 age group.
- The relative frequency of females in the 35+ age group compared with the total number of students, expressed as a percentage, is 10.86%.
