If the sum of $10$ observations and the sum of their squares are $12$ and $18$ respectively,then the standard deviation of the observations is:

If the variance of the terms in an increasing $A.P.$,$b_{1}, b_{2}, b_{3}, \ldots, b_{11}$ is $90$,then the common difference of this $A.P.$ is

The average marks of $10$ students in a class was $60$ with a standard deviation of $4$,while the average marks of another $10$ students was $40$ with a standard deviation of $6$. If all the $20$ students are taken together,their combined standard deviation will be:

Statement $1$: The variance of the first $n$ odd 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 $\frac{n(4n^2 - 1)}{3}$.

Assertion $(A)$: The variance of the first $n$ odd natural numbers is $\frac{n^2-1}{3}$.
Reason $(R)$: 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 $\frac{n(4n^2-1)}{3}$.
Which of the following alternatives is correct?

For $20$ observations of variable $x$,if $\sum(x_{i}-2)=20$ and $\sum(x_{i}-2)^2=100$,then the standard deviation of variable $x$ is