If the standard deviation of a population is 6.5, what would be the population variance?
A. 40.25
B. 42.25
C. 18.25
D. 13

Options

A. D
B. C
C. B
D. A

Answer

To find the population variance when the standard deviation is given, we can use the formula:

**Variance (σ²) = (Standard Deviation (σ))²**

Given that the standard deviation (σ) is 6.5, we can substitute this value into the formula.

### Step-by-Step Solution:

1. **Identify the standard deviation**:
- The standard deviation (σ) is given as 6.5.

2. **Apply the formula for variance**:
- We use the formula for variance:
\[ \text{Variance} = \sigma^2 \]

3. **Calculate the square of the standard deviation**:
- Now, we calculate:
\[ \text{Variance} = (6.5)^2 \]

4. **Perform the calculation**:
- Squaring 6.5:
\[ 6.5 \times 6.5 = 42.25 \]

5. **Conclusion**:
- Therefore, the population variance is 42.25.

### Final Answer:
- The population variance is **42.25**, which corresponds to option **B**.

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