Let $a, b, c, d$ and $e$ be the observations with mean $m$ and standard deviation $S$. The standard deviation of the observations $a+k, b+k, c+k, d+k$ and $e+k$ is

Find the variance of the first $n$ natural numbers.

The following is the record of goals scored by team $A$ in a football session:

No. of goals scored	$0, 1, 2, 3, 4$
No. of matches	$1, 9, 7, 5, 3$

For team $B$,the mean number of goals scored per match was $2$ with a standard deviation of $1.25$ goals. Find which team may be considered more consistent?

The marks obtained by students $A$ and $B$ in $3$ examinations are given below:

Marks of $A$	$30, 20, 40$
Marks of $B$	$70, 0, 5$

The ratio of the coefficient of variation of marks of $A$ and the coefficient of variation of marks of $B$ is:

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

In a discrete data,$\frac{1}{4}$ of the observations are equal to $a$,another $\frac{1}{4}$ of the observations are equal to $-a$. Out of the remaining,half of them are equal to $b$ and the rest are equal to $-b$. If the variance of all the observations is $ab$,then: