UPSC NDA I 2018 Mathematics Solved Paper

Concept:Mean depends on both change of origin and scale; variance depends on scale but is independent of change of origin.Explanation:For mean:If a constant $C$ is added or subtracted from each observation, the mean increases or decreases by $C$.If each observation is multiplied or divided by $C$, the mean is multiplied or divided by $C$.Thus, mean is affected by both change of origin and change of scale; it is not independent of either.Hence statement 1 (“Mean is independent of change in scale and change in origin”) is false.For variance:If a constant $C$ is added to each observation, $\text{Var}(X+C)=\text{Var}(X)$ — variance remains unchanged (independent of origin).If each observation is multiplied by $C$, $\text{Var}(CX)=C^{2}\text{Var}(X)$ — variance changes with scale (dependent on scale).Statement 2 says “Variance is independent of change in scale but not in origin” — this is exactly backwards: variance is independent of origin but dependent on scale. So statement 2 is also false.Answer:Neither statement 1 nor statement 2 is correct.