Question

The standard deviation of 25 numbers is $ \sigma $. If each of the numbers is increased by 5, then the new standard deviation will be

• A. 40
• B. 45
• C. \( 40 + \frac{21}{25} \)
• D. None of these

Hint:

When a constant is added or subtracted to every data point in a dataset, it does not affect the standard deviation, only the mean.

Answer 1

The Correct Option is A

We are given that the standard deviation of 25 numbers is \( \sigma \).
We are also told that each of the numbers is increased by 5.
Step 1: Understand the impact of adding a constant to the data
Adding a constant (in this case, 5) to each data point in a set does not change the spread of the data.
Therefore, the new standard deviation remains the same.
Step 2: Conclusion
Since the addition of a constant does not affect the standard deviation, the new standard deviation will be the same as the original standard deviation, which is \( 40 \).
Thus, the correct answer is option (a).