If the standard deviation of a population is 3 , what would be the population variance ?

Options

A. 9
B. 6
C. 8
D. 15

Answer

To find the population variance when the standard deviation is given, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The variance of a population is defined as the square of the standard deviation. The formula is:
\[ \text{Variance} = (\text{Standard Deviation})^2 \]

2. **Identify the Given Value**: In this problem, the standard deviation of the population is given as 3.

3. **Apply the Formula**: Substitute the value of the standard deviation into the formula:
\[ \text{Variance} = (3)^2 \]

4. **Calculate the Square**: Now, calculate the square of 3:
\[ \text{Variance} = 3 \times 3 = 9 \]

5. **Conclusion**: Therefore, the population variance is 9.

### Final Answer:
The population variance is **9**.