Before deciding on a theme for the upcoming senior prom, the committee decides to 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**. 

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To determine the number of students to survey from each grade for a stratified sample based on 75% of the population, we need to follow these steps:

1. Determine the total number of students.
2. Calculate 75% of the total number of students.
3. Distribute the number of students to be surveyed proportionally based on the enrolment in each grade.

Let's assume the enrolment numbers are as follows:

- Grade 11: \( n_{11} \) students
- Grade 12: \( n_{12} \) students

### Steps to calculate the stratified sample:

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

\[ n_{total} = n_{11} + n_{12} \]

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

\[ n_{sample} = 0.75 \times n_{total} \]

3. **Calculate the proportion of students to survey from each grade:**

\[ \text{Proportion of Grade 11} = \frac{n_{11}}{n_{total}} \]
\[ \text{Proportion of Grade 12} = \frac{n_{12}}{n_{total}} \]

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

\[ n_{sample11} = n_{sample} \times \frac{n_{11}}{n_{total}} \]
\[ n_{sample12} = n_{sample} \times \frac{n_{12}}{n_{total}} \]

### Example Calculation:
Let's assume there are 120 students in Grade 11 and 80 students in Grade 12.

1. **Total number of students:**

\[ n_{total} = 120 + 80 = 200 \]

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

\[ n_{sample} = 0.75 \times 200 = 150 \]

3. **Proportion of students to survey from each grade:**

\[ \text{Proportion of Grade 11} = \frac{120}{200} = 0.6 \]
\[ \text{Proportion of Grade 12} = \frac{80}{200} = 0.4 \]

4. **Number of students to survey from each grade:**

\[ n_{sample11} = 150 \times 0.6 = 90 \]
\[ n_{sample12} = 150 \times 0.4 = 60 \]

Therefore, the committee should survey:
- **90 students from Grade 11**
- **60 students from Grade 12**

This ensures that the sample is proportionally representative of the student population.

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 dealing with percentages in surveys or statistics, always ensure that the sample sizes are large enough to represent the population accurately. This helps in minimizing sampling errors.

Learn how to calculate the number of students to survey from each grade using stratified sampling. This problem involves determining a representative sample based on 75% of the student population in grades 11 and 12. Includes step-by-step calculations and example scenarios.

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