If $\sum _{i=1}^5\left(x_i-6\right)=5$ and $\sum _{i=1}^5{\left(x_i-6\right)}^2=25$, then the standard deviation of observations $3x_1+\mathrm{2,} 3x_2+\mathrm{2,} 3x_3+2,$$3x_4+2$ and$3x_5+2$ is equal to

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.