JEE MATHEMATICS MCQ: STATISTICS

Let $\bar{x}, M$ and $\sigma^2$ be respectively the mean, mode and variance of $n$ observations $\mathrm{x}_1, \mathrm{x}_2, \ldots, \mathrm{x}_{\mathrm{n}}$ and $\mathrm{d}_{\mathrm{i}}=-\mathrm{x}_{\mathrm{i}}-\mathrm{a}$, $\mathrm{i}=1,2, \ldots, \mathrm{n}$, where $\mathrm{a}$ is any number.

Statement I: Variance of $d_1, d_2, \ldots d_n$ is $\sigma^2$.

Statement II: Mean and mode of $\mathrm{d}_1, \mathrm{~d}_2, \ldots \mathrm{d}_{\mathrm{n}}$ are $-\overline{\mathrm{x}}-\mathrm{a}$ and $-\mathrm{M}-\mathrm{a}$, respectively.