Let the mean and variance of the frequency distribution be $6$ and $6.8$ respectively.

$x$	$2$	$6$	$8$	$9$
$f$	$4$	$4$	$\alpha$	$\beta$

If $x_{3}$ is changed from $8$ to $7$,then the mean for the new data will be:

The mean of a data set consisting of $20$ observations is $40$. If one observation $53$ was wrongly recorded as $33$,then the correct mean will be

Let $y_1, y_2, y_3, \dots, y_n$ be $n$ observations. Let $w_i = l y_i + k$ for all $i = 1, 2, 3, \dots, n$,where $l$ and $k$ are constants. If the mean of $y_i$ is $48$ and their standard deviation is $12$,and the mean of $w_i$ is $55$ and their standard deviation is $15$,then the values of $l$ and $k$ are:

If the mean and the variance of the data are $\mu$ and $19$ respectively,then the value of $\lambda+\mu$ is:

Class	$4-8$	$8-12$	$12-16$	$16-20$
Frequency	$3$	$\lambda$	$4$	$7$

The mean and standard deviation of $20$ observations were calculated as $10$ and $2.5$ respectively. It was found that by mistake one data value was taken as $25$ instead of $35$. If $\alpha$ and $\sqrt{\beta}$ are the mean and standard deviation respectively for the correct data,then $(\alpha, \beta)$ is:

If $\alpha$ and $\beta$ are respectively the mean deviation about the mean and the variance of the first five prime numbers,then the ordered pair $(\alpha, \beta)$ is: