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.