survey the grade 11 and 12 students. The following table shows the enrolment in the school. They decide to conduct a stratified survey based on 75% of the population. Determine the number of students they need to survey from each grade in order to represent a **stratified sample**. **Grade**

**Number of Students**

**Number Surveyed**

Grade 11

546

 90

Grade 12

482

 60

Total



To determine the number of students to survey from each grade in order to represent a stratified sample based on 75% of the population, let's follow the same steps using the provided enrollment data.

### Given Data:
- **Grade 11**: 546 students
- **Grade 12**: 482 students

### Steps:

1. **Calculate the total number of students**:

\[ n_{\text{total}} = 546 + 482 = 1028 \]

2. **Calculate 75% of the total number of students**:

\[ n_{\text{sample}} = 0.75 \times 1028 = 771 \]

3. **Calculate the proportion of students in each grade**:

\[ \text{Proportion of Grade 11} = \frac{546}{1028} \approx 0.531 \]
\[ \text{Proportion of Grade 12} = \frac{482}{1028} \approx 0.469 \]

4. **Determine the number of students to survey from each grade**:

\[ n_{\text{sample11}} = 771 \times 0.531 \approx 409.401 \]
\[ n_{\text{sample12}} = 771 \times 0.469 \approx 361.599 \]

### Rounded to the nearest whole number:
\[ n_{\text{sample11}} \approx 409 \]
\[ n_{\text{sample12}} \approx 362 \]

### Result:
- **Number of students to survey from Grade 11**: 409
- **Number of students to survey from Grade 12**: 362

This ensures a proportionally representative sample of 75% of the student population from each grade.

Would you like more details or have any questions? Here are some questions you might want to ask next:

1. What are the benefits of using a stratified sampling method?
2. How would the calculations change if the percentages were different?
3. Can you explain more about the different types of sampling methods?
4. How would you handle a situation where the total number of students isn't an exact multiple of the sample size?
5. What are the potential sources of bias in a stratified sample?

**Tip:** When using stratified sampling, ensure that the strata (groups) are mutually exclusive and collectively exhaustive to achieve an accurate representation of the entire population.

Learn how to conduct a stratified survey of Grade 11 and 12 students based on enrollment data. Determine the number of students needed to survey from each grade to achieve a 75% representative sample. Includes detailed calculations and methods for proportional sampling.

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