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The image you uploaded presents a data set of exam scores, along with the sample mean of 83.5 and a sample standard deviation of 16. The question is asking why Chebyshev's Rule was applied for this data set.

### Chebyshev’s Rule Explanation:
Chebyshev's Rule, or Chebyshev's Theorem, applies to any data distribution, regardless of its shape. This is a key difference between Chebyshev's Rule and the Empirical Rule, which only applies to normal (bell-shaped) distributions. Chebyshev’s Theorem states that for any data set, at least \(1 - \frac{1}{k^2}\) of the data lies within \(k\) standard deviations of the mean, where \(k > 1\).

### Answer Explanation:
- **The reason for using Chebyshev's Rule here** is likely because **the data set is not symmetric**. In cases where the data does not follow a normal distribution (symmetry), the Empirical Rule (which assumes normality) is not appropriate. Chebyshev’s Rule is used because it applies universally to all data sets, symmetric or not.
  
### Conclusion:
The correct answer would be **"The data set was not symmetric."**

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### 5 Related Questions:
1. What are the conditions for applying the Empirical Rule versus Chebyshev’s Rule?
2. How does the shape of a data distribution affect the choice of statistical rules?
3. Can Chebyshev's Rule give more precise estimates for symmetric data distributions?
4. What percentage of data lies within 2 standard deviations according to Chebyshev’s Rule?
5. How do you calculate the standard deviation of a sample manually?

### Tip:
If your data appears skewed or non-normal, always consider using Chebyshev's Rule instead of the Empirical Rule for making predictions about the data distribution.

Consider the following sample data set of exam scores, where the sample mean is 83.5 and the sample standard deviation is 16. Why did we use Chebyshev's Rule for this data set?

Explore why Chebyshev's Rule is used for a non-symmetric data set of exam scores with a sample mean of 83.5 and a standard deviation of 16. Understand key statistical concepts, formulas, and theorems related to data distribution. Suitable for Grades 9-12.

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