Question

Let $x_1 , x_2,...., x_n$ be n observations, and let $\bar{x}$ be their arithmetic mean and $\sigma^2$ be the variance. Variance of $2x_1, 2x_2, ..., 2x_n$ is $4 \sigma^2$. Arithmetic mean $2x_1, 2x_2, ..., 2x_n$ is 4 $\bar{x}$ .

• A. Statement-1 is false, Statement-2 is true
• B. Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1
• C. Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for Statement-1
• D. Statement-1 is true, statement-2 is false

Answer 1

Answer: (D)

Statement-1 is true, statement-2 is false

Answer 2

If each observation is multiplied by k, mean gets multiplied by k and variance gets multiplied by $k^2$. Hence the new mean should be $2 \bar{x}$ and new variance should be $k^2 \sigma^2$. So statement-1 is true and statement-2 is false.