If the variance of a data is 256, then the standard deviation is

Options

A. 15
B. 16
C. 13
D. 14

Answer

To find the standard deviation from the variance, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between variance and standard deviation**:
- The variance (denoted as \( \sigma^2 \)) is related to the standard deviation (denoted as \( \sigma \)) by the formula:
\[ \sigma = \sqrt{\sigma^2} \]
- This means that the standard deviation is the square root of the variance.

2. **Identify the given variance**:
- In this problem, we are given that the variance is \( 256 \).

3. **Apply the formula to find the standard deviation**:
- Substitute the given variance into the formula:
\[ \sigma = \sqrt{256} \]

4. **Calculate the square root**:
- Now, we need to calculate the square root of \( 256 \):
\[ \sqrt{256} = 16 \]

5. **Conclusion**:
- Therefore, the standard deviation is \( 16 \).

### Final Answer:
The standard deviation is \( 16 \).

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