The mean and standard deviation of $15$ observations are found to be $8$ and $3$ respectively. On rechecking,it was found that,in the observations,$20$ was misread as $5$. Then,the correct variance is equal to......

The variance of the observations $112, 116, 120, 125, 132$ is $......$

The sum of $100$ observations and the sum of their squares are $400$ and $2475$,respectively. Later on,three observations,$3, 4$ and $5$,were found to be incorrect. If the incorrect observations are omitted,then the variance of the remaining observations is

If the variance of the numbers $2, 3, 11$ and $x$ is $\frac{49}{4}$,then the values of $x$ are

The variance of $50$ observations is $7$. Suppose that each observation in this data is multiplied by $6$ and then $5$ is subtracted from it. Then the variance of that new data is

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