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

  • [JEE MAIN 2014]
  • 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

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