Let the mean of the data be $5$.

$X$	$1$	$3$	$5$	$7$	$9$
$f$	$4$	$24$	$28$	$\alpha$	$8$

If $m$ and $\sigma^2$ are respectively the mean deviation about the mean and the variance of the data,then $\frac{3 \alpha}{m+\sigma^2}$ is equal to $..........$.

The mean and variance of the observations $x_1, x_2, x_3, \ldots, x_{15}$ are respectively $2$ and $4$. If the mean and variance of the observations $y_1, y_2, \ldots, y_{10}$ are respectively $2$ and $5$,then the variance of the combined observations $x_1, x_2, \ldots, x_{15}, y_1, y_2, \ldots, y_{10}$ is

If the coefficients of variation of two distributions are $40$ and $20$ and their variances are $144$ and $64$ respectively,then the mean of their arithmetic means is

For $(2n+1)$ observations ${x_1}, -{x_1}, {x_2}, -{x_2}, ....., {x_n}, -{x_n}$ and $0$,where all $x_i$ are distinct,let $S.D.$ and $M.D.$ denote the standard deviation and median respectively. Which of the following is always true?

If $x_1, x_2, \ldots, x_n$ are $n$ observations such that $\sum_{i=1}^n x_i^2 = 400$ and $\sum_{i=1}^n x_i = 80$,then the least value of $n$ is

$\bar{x}$ and $\bar{y}$ are the arithmetic means of the runs of two batsmen $A$ and $B$ in $10$ innings respectively,and $\sigma_{A}$ and $\sigma_{B}$ are the standard deviations of their runs. If batsman $A$ is more consistent than $B$,then he is also a higher run scorer only when