Find the variance for the data

$x_i$	$6$	$10$	$14$	$18$	$24$	$28$	$30$
$f_i$	$2$	$4$	$7$	$12$	$8$	$4$	$3$

 

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.