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Let's solve the problem based on the given data.

### Data:
- One-Year CD Yields: 5.36, 5.32, 5.30, 5.31, 5.24
- Five-Year CD Yields: 5.94, 5.90, 5.84, 5.84, 5.78

### Part (a) Compute for One-Year and Five-Year CDs:
1. **Variance**
2. **Standard Deviation**
3. **Range**
4. **Coefficient of Variation (CV)**

---

#### 1. **Variance** Formula:
\[
\sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2
\]
Where \( \bar{x} \) is the mean of the data.

#### 2. **Standard Deviation (SD)**:
\[
\sigma = \sqrt{\text{Variance}}
\]

#### 3. **Range**:
\[
\text{Range} = \text{Max value} - \text{Min value}
\]

#### 4. **Coefficient of Variation (CV)**:
\[
\text{CV} = \frac{\sigma}{\bar{x}} \times 100\%
\]

I'll compute these values for both the One-Year and Five-Year CDs. Let's start with the One-Year CD data first. I'll calculate everything step by step.### Calculations for One-Year and Five-Year CDs:

#### One-Year CDs:
- **Mean**: 5.306
- **Variance**: 0.00150
- **Standard Deviation**: 0.03878
- **Range**: 0.12
- **Coefficient of Variation (CV)**: 0.731%

#### Five-Year CDs:
- **Mean**: 5.86
- **Variance**: 0.00304
- **Standard Deviation**: 0.05514
- **Range**: 0.16
- **Coefficient of Variation (CV)**: 0.941%

### Part (b) Explanation:
Based on the results, the **Five-Year CDs** have a larger variance, standard deviation, and coefficient of variation, indicating that the yields for Five-Year CDs have **more variation** compared to the One-Year CDs.

Would you like more details on any step, or have any questions?

### 5 Related Questions:
1. How do you interpret variance in data?
2. Why is the coefficient of variation useful when comparing data sets with different means?
3. What is the relationship between variance and standard deviation?
4. How does range differ from standard deviation in terms of measuring spread?
5. Can high variability in CD rates impact investment decisions?

### Tip:
When comparing datasets with different means, the coefficient of variation (CV) is a better measure of relative variability than standard deviation.

For one-year CDs and five-year CDs, separately compute the variance, standard deviation, range, and coefficient of variation. Based on the results, do one-year CDs or five-year CDs have more variation in the highest yields offered? Explain.

Compute the variance, standard deviation, range, and coefficient of variation for one-year and five-year CDs to determine which has more variation in yields. Includes detailed statistical analysis and step-by-step calculations. Suitable for Grades 11-12 or college-level statistics.

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