The arithmetic mean of marks in Mathematics for four divisions $A, B, C$ and $D$ were $80, 75, 70$ and $72$ respectively. Their standard deviations were $12, 6, 8$ and $10$ respectively. Then,which division has more uniformity?

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

The standard deviation of the first $n$ odd natural numbers is ..........

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?

If the mean of the numbers $a, b, 8, 5, 10$ is $6$ and the variance is $6.80$,then which of the following is a possible value for $a$ and $b$?

The variance of $20$ observations is $5$. If each of the observations is multiplied by $2$,then the variance of the resulting observations is: