If the mean and variance of the frequency distribution are $9$ and $15.08$ respectively,then the value of $\alpha^2+\beta^2-\alpha \beta$ is $............$.

$x_i$	$2$	$4$	$6$	$8$	$10$	$12$	$14$	$16$
$f_i$	$4$	$4$	$\alpha$	$15$	$8$	$\beta$	$4$	$5$

The mean age of $25$ teachers in a school is $40$ years. $A$ teacher retires at the age of $60$ years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is $39$ years,then the age (in years) of the newly appointed teacher 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

Consider a set of $3n$ numbers having variance $4$. In this set,the mean of the first $2n$ numbers is $6$ and the mean of the remaining $n$ numbers is $3$. $A$ new set is constructed by adding $1$ to each of the first $2n$ numbers and subtracting $1$ from each of the remaining $n$ numbers. If the variance of the new set is $k$,then $9k$ is equal to .... .

Statement $(I)$: The range of the ungrouped data does not change even if certain intermediate observations are removed.
Statement $(II)$: The value of the mean deviation of an ungrouped data about the median is always less than or equal to the value of the mean deviation computed about any other measure of central tendency.
Statement $(III)$: For a grouped data,range is approximated as the difference between the lower limit of the largest class and the upper limit of the smallest class.

Let $r$ be the range and $S^2 = \frac{1}{n - 1} \sum_{i = 1}^n (x_i - \bar{x})^2$ be the variance of a set of observations $x_1, x_2, \dots, x_n$. Then: