The image provided contains a table with information about different grade levels, the number of students in each grade, and corresponding sample sizes. Let's extract the dataThe image provided contains a table with information about different grade levels, the number of students in each grade, and corresponding sample sizes. Let's extract the

Table Data:

1. Grade Level:
   • 7, 8, 9, 10
2. Number of Students (No. of Students):
   • For Grade 7: 823
   • For Grade 8: 922
   • For Grade 9: 1,020
   • For Grade 10: 1,000
   • Total Number of Students (N): 3,765
3. Sample Sizes:
   • For Grade 7: 273
   • For Grade 8: 280
   • For Grade 9: 285
   • For Grade 10: 281

Formula:

It appears that a formula is given: $n = \frac{N}{1 + N \cdot (5\%)^2}$

This formula is used to determine the sample size, where:

• $N$ is the total population size.
• $5\%$ is the assumed margin of error or confidence interval (which is 0.05 when converted to decimal).

Calculation:

Let's calculate the overall sample size using this formula.

$n = \frac{3765}{1 + 3765 \cdot (0.05)^2}$

$n = \frac{3765}{1 + 3765 \cdot 0.0025}$

$n = \frac{3765}{1 + 9.4125}$

$n = \frac{3765}{10.4125} \approx 361.63$

The total sample size rounded to the nearest whole number is approximately 362.

Would you like more details about these calculations, or do you have any specific questions?

Related Questions to Consider:

1. How does the sample size change if we change the margin of error (e.g., to 4% or 6%)?
2. What would be the effect of using different confidence levels (e.g., 90% vs. 95%) on the sample size?
3. How are these sample sizes practically chosen for each grade level?
4. Why is a sample size calculation important in statistics?
5. How can we apply this sample size calculation to other populations?

Tip:

Always ensure that your sample size is representative of the population to maintain the accuracy of the results.