The following data was collected from a newspaper: (percentage distribution). It is an example of

$Country$	$Agriculture$	$Industries$	$Services$	$Others$
$India$	$45$	$19$	$28$	$4$
$U.K.$	$3$	$40$	$44$	$13$
$Japan$	$6$	$48$	$43$	$3$
$U.S.A.$	$3$	$35$	$61$	$1$

Consider the following frequency distribution:

Value	$4$	$5$	$8$	$9$	$6$	$12$	$11$
Frequency	$5$	$f_1$	$f_2$	$2$	$1$	$1$	$3$

Suppose that the sum of the frequencies is $19$ and the median of this frequency distribution is $6$. For the given frequency distribution,let $\alpha$ denote the mean deviation about the mean,$\beta$ denote the mean deviation about the median,and $\sigma^2$ denote the variance. Match each entry in List-$I$ to the correct entry in List-$II$ and choose the correct option.

List-$I$	List-$II$
$(P) \ 7f_1+9f_2$ is equal to	$(1) \ 146$
$(Q) \ 19\alpha$ is equal to	$(2) \ 47$
$(R) \ 19\beta$ is equal to	$(3) \ 48$
$(S) \ 19\sigma^2$ is equal to	$(4) \ 145$
	$(5) \ 55$

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

If the sum of the deviations of $50$ observations from $30$ is $50$,then the mean of these observations is:

The mean of $9$ observations is $15$. If a new observation is added,the new mean becomes $16$. What is the value of the new observation?

The average incomes of the people in two villages are $P$ and $Q$,respectively. Assume that $P \neq Q$. $A$ person moves from the first village to the second village. The new average incomes are $P^{\prime}$ and $Q^{\prime}$,respectively. Which of the following is not possible?