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The problem asks to find the standard error of the average IQ of 81 students when the population average IQ is 105 and the population standard deviation is 15.

The formula for the **standard error of the mean (SE)** is:

\[
SE = \frac{\sigma}{\sqrt{n}}
\]

Where:
- \(\sigma\) is the population standard deviation (15),
- \(n\) is the sample size (81).

### Step-by-step calculation:

1. \(\sigma = 15\),
2. \(n = 81\),
3. Calculate the square root of the sample size: \(\sqrt{81} = 9\),
4. Now, apply the formula:

\[
SE = \frac{15}{9} = 1.6667
\]

Thus, the standard error is approximately **1.6667**.

### Correct answer: **Option D**.

Would you like further details or have any questions about this problem?

Here are 5 related questions:
1. How does the standard error change if the sample size increases?
2. What is the significance of a small standard error in a data set?
3. How does the standard deviation affect the standard error?
4. Can you calculate the confidence interval using the standard error?
5. How would this calculation change if the population standard deviation was unknown?

**Tip:** The standard error decreases as the sample size increases, meaning larger samples provide more precise estimates of the population mean.

In a particular large school system, the average IQ of elementary school children is 105 and the standard deviation is 15. If 81 children were selected at random from elementary schools within the system, what is the standard error of the average IQ of 81 students?

Learn how to calculate the standard error of the average IQ of 81 students, given a population IQ average of 105 and a standard deviation of 15. This problem uses statistical concepts such as the standard error formula and is suitable for Grades 10-12.

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