Statistics
Change of Scale and Origin
IIT-JEE 1988
Grade 11
Question:
The mean and standard deviation of 100 observations are 50 and 5 respectively. If 5 is added to every observation, the new mean and standard deviation are:
(1) mean 55, S.D. 5
(2) mean 55, S.D. 10
(3) mean 50, S.D. 5
(4) mean 55, S.D. 0
Step-by-Step Solution
Key Concept: Recall how the mean and the standard deviation each respond to adding the same constant to every observation — one of them shifts, the other does not change at all.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)