Statistics
Change of Scale and Origin
Premium Question
Grade 11
Question:
If a data set has variance $\sigma^2$, and a constant 5 is added to every observation, then the variance of the new data set is:
(1) $\sigma^2 + 25$
(2) $\sigma^2$
(3) $\sigma^2 + 5$
(4) $25\sigma^2$
Step-by-Step Solution
Key Concept: Adding the same constant to every observation shifts each value, and hence the mean, by that constant — but think about what happens to the differences $x_i - \bar{x}$, which is what variance actually depends on.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)