Statistics
Change of Scale and Origin
Premium Question
Grade 11
Question:
If a data set has standard deviation $\sigma$, and every observation is multiplied by 2, then the standard deviation of the new data set is:
(1) $\sigma$
(2) $2\sigma$
(3) $4\sigma$
(4) $\frac{\sigma}{2}$
Step-by-Step Solution
Key Concept: Standard deviation has the same units as the data itself, so multiplying every observation by a constant $k$ scales the standard deviation by $|k|$ (unlike variance, which scales by $k^2$).
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)