To determine the marginal relative frequency for students who plan to attend college, we should follow these steps:
1. Understand the two-way table:
The table summarizes the survey data:
- College: Students who plan to attend college.
- Not College: Students who do not plan to attend college.
- Travel & Not Travel: The secondary plans of these students.
- Totals: Totals in each category and overall.
The totals given are:
- Total number of students who plan to attend college: 67
- Total number of students surveyed: 82
2. Calculate the marginal relative frequency:
This is the ratio of the number of students who plan to attend college to the total number of surveyed students, multiplied by 100 to get the percentage:
[tex]\[
\text{Marginal Relative Frequency} = \left(\frac{\text{Number of college students}}{\text{Total number of students}} \right) \times 100
\][/tex]
Substituting the numbers:
[tex]\[
\text{Marginal Relative Frequency} = \left(\frac{67}{82}\right) \times 100
\][/tex]
3. Get the exact percentage:
[tex]\[
\left(\frac{67}{82}\right) \times 100 \approx 81.70731707317073
\][/tex]
4. Round the percentage to the nearest whole number:
[tex]\[
81.70731707317073 \text{ rounded to the nearest percent is } 82\%
\][/tex]
So, the marginal relative frequency for students who plan to attend college, rounded to the nearest percent, is 82%. Thus, neither 18% nor 22% are correct. The correct percentage is 82%.
