Let $\bar{x}, M$ and $\sigma^2$ be respectively the mean,mode and variance of $n$ observations $x_1, x_2, ..., x_n$ and $d_i = -x_i - a, i = 1, 2, ..., n$,where $a$ is any number. Statement $I$: Variance of $d_1, d_2, ..., d_n$ is $\sigma^2$. Statement $II$: Mean and mode of $d_1, d_2, ..., d_n$ are $-\bar{x} - a$ and $-M - a$,respectively.

• A
  Statement $I$ and Statement $II$ are both false
• B
  Statement $I$ and Statement $II$ are both true
• C
  Statement $I$ is true and Statement $II$ is false
• D
  Statement $I$ is false and Statement $II$ is true