The mean and standard deviation of $100$ items are $50$ and $4$,respectively. Find the sum of all the items and the sum of the squares of the items.

The standard deviation of $25$ numbers is $40$. If each of the numbers is increased by $5$,then the new standard deviation will be

Determine the mean and standard deviation for the following distribution:
$\begin{array}{|l|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \text{Marks} & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 \\ \hline \text{Frequency} & 1 & 6 & 6 & 8 & 8 & 2 & 2 & 3 & 0 & 2 & 1 & 0 & 0 & 0 & 1 \\ \hline \end{array}$

If the mean of the frequency distribution is $28$,then its variance is $........$.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$2$	$3$	$x$	$5$	$4$

Given that the total of $16$ values is $528$ and the sum of the squares of deviations from $33$ is $9158$. The variance is:

The variance of the following distribution is:

Marks	$1-3$	$3-5$	$5-7$	$7-9$
Number of students	$40$	$30$	$20$	$10$