If the mean and standard deviation of $n$ observations $x_1, x_2, \dots, x_n$ are $\bar{x}$ and $\sigma$ respectively,then what is the sum of the squares of the observations?

Find the variance of the sequence $a, a + d, a + 2d, \dots, a + 2nd$.

If $\sum_{i = 1}^9 (x_i - 5) = 9$ and $\sum_{i = 1}^9 (x_i - 5)^2 = 45$,then the standard deviation of the $9$ items $x_1, x_2, ..., x_9$ is:

For the following frequency distribution,the variance is approximately equal to

Class Interval	$0$-$5$	$5$-$10$	$10$-$15$	$15$-$20$	$20$-$25$
Frequency	$4$	$1$	$10$	$3$	$2$

Find the variance of the following data: $6, 8, 10, 12, 14, 16, 18, 20, 22, 24$

$A$ 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?