If the arithmetic mean of the following frequency distribution is $50$,find the values of $f_1$ and $f_2$.

Class	Frequency
$0 - 20$	$17$
$20 - 40$	$f_1$
$40 - 60$	$32$
$60 - 80$	$f_2$
$80 - 100$	$19$
Total	$120$

The mean and variance of the marks obtained by $n$ students in a test are $10$ and $4$ respectively. Later,the marks of one of the students is increased from $8$ to $12$. If the new mean of the marks is $10.2$,then their new variance is equal to:

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 $...........$

Find the range of the given numbers: $10, 8, 12, 11, 14, 9, 6$.

Consider the following data:

Daily wage (Rs.)	$30$-$40$	$40$-$50$	$50$-$60$	$60$-$70$	$70$-$80$	$80$-$90$
No. of workers	$17$	$28$	$21$	$15$	$13$	$6$

The coefficient of variation of the above distribution of wages,if its standard deviation is $14.72$,is

If both mean and variance of $50$ observations $x_1, x_2, \ldots, x_{50}$ are equal to $16$ and $256$ respectively,then the mean of $(x_1-5)^2, (x_2-5)^2, \ldots, (x_{50}-5)^2$ is