To find the variance of \( S^2(x/2) = 2 \), let's walk through the interpretation and solution process step by step.

1. **Step 1: Recognizing the notation \( S^2 \)**  
   Here, \( S^2 \) is typically used to represent the sample variance of a dataset. Given that it's a function of \( \frac{x}{2} \), the equation suggests that the variance of \( \frac{x}{2} \) is equal to 2.

2. **Step 2: Variance of a scaled random variable**  
   The variance of a random variable that is scaled by a constant \( c \) follows this rule:  
   \[
   \text{Var}(cX) = c^2 \cdot \text{Var}(X)
   \]
   In this case, \( X = x \) and the scaling factor is \( \frac{1}{2} \). Therefore,  
   \[
   \text{Var}\left(\frac{x}{2}\right) = \left(\frac{1}{2}\right)^2 \cdot \text{Var}(x) = \frac{1}{4} \cdot \text{Var}(x)
   \]

3. **Step 3: Solve for the variance of \( x \)**  
   From the equation \( \text{Var}\left(\frac{x}{2}\right) = 2 \), we substitute the variance formula:  
   \[
   \frac{1}{4} \cdot \text{Var}(x) = 2
   \]
   Now, solve for \( \text{Var}(x) \):
   \[
   \text{Var}(x) = 2 \times 4 = 8
   \]

Thus, the **variance of \( x \)** is \( \boxed{8} \).

Would you like more details on this or have any follow-up questions?

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Here are 5 related questions that expand on this concept:
1. How does the variance of a random variable change when multiplied by a constant?
2. What is the difference between sample variance and population variance?
3. How do you calculate the variance of a dataset?
4. Can you explain the properties of variance for independent random variables?
5. What is the relationship between standard deviation and variance?

**Tip:** Remember that variance is always non-negative, as it measures the spread of data squared.

This problem explores the concept of variance, specifically how scaling a random variable affects its variance. Follow a detailed step-by-step solution to find the variance of x, using the variance scaling formula Var(cX) = c^2 * Var(X). Suitable for advanced high school or college-level students.

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