Question

The standard deviation of a distribution is 5. If each observation is increased by 2, then the new standard deviation will be:

• A. 5
• B. 7
• C. 3
• D. 10

Hint:

Adding or subtracting a constant changes only the mean. Multiplying every observation by a constant \(k\) changes the standard deviation to \[ |k|\sigma. \]

Answer 1

The Correct Option is A

Step 1: Determine the given information. Original standard deviation: \[ \sigma=5. \] Each observation is increased by \[ 2. \]

Step 2: Apply the property of standard deviation. Since adding a constant does not affect dispersion, \[ \text{New Standard Deviation} = \text{Old Standard Deviation}. \] Therefore, \[ \sigma_{\text{new}} = 5. \] Conclusion: \[ {5} \] Hence, the correct answer is Option (A).