For the frequency distribution :

Variate $( x )$	$x _{1}$	$x _{1}$	$x _{3} \ldots \ldots x _{15}$
Frequency $(f)$	$f _{1}$	$f _{1}$	$f _{3} \ldots f _{15}$

where $0< x _{1}< x _{2}< x _{3}<\ldots .< x _{15}=10$ and

$\sum \limits_{i=1}^{15} f_{i}>0,$ the standard deviation cannot be 

Let the mean and the variance of 6 observation $a, b$, $68,44,48,60$ be $55$ and $194 $, respectively if $a>b$, then $a+3 b$ is

Let sets $A$ and $B$ have $5$ elements each. Let the mean of the elements in sets $A$ and $B$ be $5$ and $8$ respectively and the variance of the elements in sets $A$ and $B$ be $12$ and $20$ respectively $A$ new set $C$ of $10$ elements is formed by subtracting $3$ from each element of $A$ and adding 2 to each element of B. Then the sum of the mean and variance of the elements of $C$ is $.......$.

Determine the mean and standard deviation for the following distribution:

$\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|} \hline \text { Marks } & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 \\ \hline \text { Frequency } & 1 & 6 & 6 & 8 & 8 & 2 & 2 & 3 & 0 & 2 & 1 & 0 & 0 & 0 & 1 \\ \hline \end{array}$

The variance of the first $n$ natural numbers is

Find the variance and standard deviation for the following data: