To determine how many more Year 9 students than Year 8 students should be in Mr. Ford's stratified survey, we need to follow these steps:
1. Calculate the Proportion of Students in Each Year Group:
- For Year 7:
[tex]\[
\text{Proportion of Year 7 students} = \frac{\text{Number of Year 7 students}}{\text{Total number of students}} = \frac{80}{350} \approx 0.229
\][/tex]
- For Year 8:
[tex]\[
\text{Proportion of Year 8 students} = \frac{\text{Number of Year 8 students}}{\text{Total number of students}} = \frac{110}{350} \approx 0.314
\][/tex]
- For Year 9:
[tex]\[
\text{Proportion of Year 9 students} = \frac{\text{Number of Year 9 students}}{\text{Total number of students}} = \frac{160}{350} \approx 0.457
\][/tex]
2. Determine the Number of Students to Survey from Each Year Group:
Since Mr. Ford wants to survey a total of 50 students, we will multiply the total survey size by the proportion for each year group.
- For Year 7:
[tex]\[
\text{Number of Year 7 students to survey} = 50 \times 0.229 \approx 11.43
\][/tex]
- For Year 8:
[tex]\[
\text{Number of Year 8 students to survey} = 50 \times 0.314 \approx 15.71
\][/tex]
- For Year 9:
[tex]\[
\text{Number of Year 9 students to survey} = 50 \times 0.457 \approx 22.86
\][/tex]
3. Calculate the Difference Between the Number of Year 9 and Year 8 Students in the Survey:
- Difference between Year 9 and Year 8 students:
[tex]\[
\text{Difference} = \text{Number of Year 9 students to survey} - \text{Number of Year 8 students to survey} \approx 22.86 - 15.71 = 7.15
\][/tex]
Therefore, there should be approximately 7.15 more Year 9 students than Year 8 students in Mr. Ford's survey.
