Let $x_1, x_2, \dots, x_{100}$ be $100$ observations such that $\sum x_i = 0$,$\sum_{1 \le i < j \le 100} |x_i x_j| = 80000$,and the mean deviation from their mean is $5$. Then their standard deviation is:

If the standard deviation of data is $12$ and mean is $72$,then the coefficient of variation is: (in $\%$)

$A$ scientist weighs $30$ fish. Their mean weight is $30 \text{ g}$ and the standard deviation is $2 \text{ g}$. Later,it is discovered that the weighing scale was not calibrated correctly and every fish's weight was recorded $2 \text{ g}$ less than the actual weight. What are the correct mean and standard deviation (in grams) of the fish weights,respectively?

The variance of the data $1, 2, 3, 5, 8, 13, 17$ is approximately

If the variance of the distribution is $45.8$,then find the variance of the distribution given below:

$x_i$	$4$	$8$	$11$	$17$	$20$	$24$	$32$
$f_i$	$3$	$5$	$9$	$5$	$4$	$3$	$1$

$y_i$	$10$	$18$	$24$	$36$	$42$	$50$	$66$
$f_i$	$3$	$5$	$9$	$5$	$4$	$3$	$1$

Statement-$1$: The variance of the first $n$ even natural numbers is $\frac{n^2 - 1}{3}$.
Statement-$2$: The sum of the first $n$ odd natural numbers is $n^2$ and the sum of the squares of the first $n$ odd natural numbers is $\frac{n(4n^2 - 1)}{3}$.