Let $x_1, x_2, ....., x_n$ be $n$ observations, and let $\overline{x}$ be their arithematic mean and $\sigma^2$ be their variance. <br> Statement 1 : Variance of $2x_1, 2x_2, ....,2x_n$ is $4 \sigma^2$ <br> Statement 2 : Arithmetic mean of $2x, 2x_2, .... , 2x_n$ is $4 \overline{x}$.

Question

( A ) Statement 1 is true, statement 2 is false
( B ) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
( C ) Statement 1 is false, statement 2 is true
( D ) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1