A data consists of $n$ observations: $x_1,x_2,\dots ,x_n.$ If $\sum _{i=1}^n{(x_i+1)}^2=11n$ and $\sum _{i=1}^n{\left(x_i-1\right)}^2=7n,$ then the variance of this data is

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.