(e) If the variance of a data is 7225, then the standard deviation of the data is ……………….

Answer

To find the standard deviation from the given 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 the square of the standard deviation (denoted as \( \sigma \)).
- Therefore, if we know the variance, we can find the standard deviation by taking the square root of the variance.

2. **Given the variance**:
- In this case, the variance is given as \( 7225 \).

3. **Set up the equation**:
- We know that \( \sigma^2 = 7225 \).

4. **Calculate the standard deviation**:
- To find \( \sigma \), we take the square root of \( 7225 \):
\[ \sigma = \sqrt{7225} \]

5. **Factor the number**:
- We can factor \( 7225 \) to simplify the square root:
\[ 7225 = 5 \times 1445 \]
\[ 1445 = 5 \times 289 \]
\[ 289 = 17 \times 17 \]
- Thus, we can rewrite \( 7225 \) as:
\[ 7225 = 5^2 \times 17^2 \]

6. **Take the square root**:
- Now, we can take the square root:
\[ \sigma = \sqrt{5^2 \times 17^2} = 5 \times 17 \]
\[ \sigma = 85 \]

### Final Answer:
The standard deviation of the data is \( 85 \).

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