The standard deviation of a distribution is 5. If each observation is increased by 2, then the new standard deviation will be:
Show Hint
- 5
- 7
- 3
- 10
The Correct Option is A
Solution and Explanation
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: \[ \boxed{5} \] Hence, the correct answer is Option (A).
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