Let $x_{1}, x_{2}, \ldots, x_{n}$ be $n$ observations, and let $\bar{x}$ be their arithmetic mean and $\sigma^{2}$ be their variance. Statement 1: Variance of $2x_{1}, 2x_{2}, \ldots, 2x_{n}$ is $4\sigma^{2}$. Statement 2: Arithmetic mean of $2x_{1}, 2x_{2}, \ldots, 2x_{n}$ is $4\bar{x}$. (1) Statement 1 is false, Statement 2 is true (2) Statement 1 is true, Statement 2 is false (3) Statement 1 is true, Statement 2 is the correct explanation for Statement 1 (4) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1
Let $x_{1}, x_{2}, \ldots, x_{n}$ be $n$ observations, and let $\bar{x}$ be their arithmetic mean and $\sigma^{2}$ be their variance. Statement 1: Variance of $2x_{1}, 2x_{2}, \ldots, 2x_{n}$ is $4\sigma^{2}$. Statement 2: Arithmetic mean of $2x_{1}, 2x_{2}, \ldots, 2x_{n}$ is $4\bar{x}$.\\
(1) Statement 1 is false, Statement 2 is true\\
(2) Statement 1 is true, Statement 2 is false\\
(3) Statement 1 is true, Statement 2 is the correct explanation for Statement 1\\
(4) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1