Let $x_1, x_2, x_3, \dots, x_n$ be $n$ observations,$\bar{x}$ be their arithmetic mean,and $\sigma^2$ be their variance.
Statement $-1$: The variance of observations $2x_1, 2x_2, 2x_3, \dots, 2x_n$ is $4\sigma^2$.
Statement $-2$: The arithmetic mean of $2x_1, 2x_2, 2x_3, \dots, 2x_n$ is $4\bar{x}$.

  • A
    Statement $-1$ is true,Statement $-2$ is true,and Statement $-2$ is $NOT$ the correct explanation for Statement $-1$.
  • B
    Statement $-1$ is true,Statement $-2$ is false.
  • C
    Statement $-1$ is false,Statement $-2$ is true.
  • D
    Statement $-1$ is true,Statement $-2$ is true,and Statement $-2$ is the correct explanation for Statement $-1$.

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