Let $\overline{x}$, $M$ 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 $-\overline{x}-a$ and $-M-a$, respectively.

• Correct answer
  A

  Statement I and Statement II are both true 
• B

  Statement I and Statement II are both false 
• C

  Statement I is true and Statement II is false
• D

  Statement I is false and Statement II is true

Hence, the correct answer is option: 'A'.