The mean of $n$ items is $\bar x$. If the first term is increased by $1$,the second by $2$,and so on,then the new mean is:

For a distribution with equal class widths,the median of $100$ observations is $25$. If the median class is $20-30$ and the number of observations less than $20$ is $45$,what is the frequency of the median class?

Let the mean and the variance of $20$ observations $x_{1}, x_{2}, \ldots, x_{20}$ be $15$ and $9$,respectively. For $\alpha \in R$,if the mean of $(x_{1}+\alpha)^{2}, (x_{2}+\alpha)^{2}, \ldots, (x_{20}+\alpha)^{2}$ is $178$,then the square of the maximum value of $\alpha$ is equal to $...........$

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 the variance of five observations are $4$ and $5.20,$ respectively. If three of the observations are $3, 4,$ and $4,$ then the absolute value of the difference of the other two observations is

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