Statistics
Change of Scale and Origin
IIT-JEE 1990
Grade 11
Question:
If every observation of a data set is multiplied by 3, then the variance of the new data set becomes how many times the variance of the original data set?
(1) 3 times
(2) 6 times
(3) 9 times
(4) 12 times
Step-by-Step Solution
Key Concept: Recall that variance has the units of $(\text{data})^2$, so multiplying every observation by a constant $k$ scales the variance by $k^2$, not by $k$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)