The standard deviation of 25 numbers is 40. If each of the numbers in increased by 5, then the new standard deviation will be -

Options

A. 40
B. 45
C. `40+(21)/(25)`
D. None of these

Explanation

To solve the problem, we need to understand the properties of standard deviation, particularly how it behaves when a constant is added to each data point.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The standard deviation of 25 numbers is given as 40.

2. **Understand the Effect of Adding a Constant:**
- When each number in a dataset is increased (or decreased) by the same constant, the standard deviation of the dataset remains unchanged. This is a fundamental property of standard deviation.

3. **Apply the Property:**
- Since we are increasing each of the 25 numbers by 5, we can conclude that the standard deviation will not change.

4. **State the New Standard Deviation:**
- Therefore, the new standard deviation remains 40.

### Final Answer:
The new standard deviation will be **40**.

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