The average incomes of the people in two vill | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the number of people in the two villages be $x$ and $y$ respectively.Given,the average income of $x$ people is $P$ and the average income of $

Vedclass · Accepted Answer

$P^{\prime} = P$ and $Q^{\prime} = Q$

Vedclass · Answer

(C) Let the number of people in the two villages be $x$ and $y$ respectively.Given,the average income of $x$ people is $P$ and the average income of $y$ people is $Q$.Therefore,the total income of people in the two villages is $Px$ and $Qy$ respectively.One person with income $I$ moves from the first village to the second village.Then,the number of people in the first village becomes $x-1$ and in the second village becomes $y+1$.The new average incomes are $P^{\prime} = \frac{Px - I}{x-1}$ and $Q^{\prime} = \frac{Qy + I}{y+1}$.If $P^{\prime} = P$,then $Px - I = P(x-1) = Px - P$,which implies $I = P$.If $Q^{\prime} = Q$,then $Qy + I = Q(y+1) = Qy + Q$,which implies $I = Q$.Since $P 
eq Q$,the person cannot have an income $I$ such that both $P^{\prime} = P$ and $Q^{\prime} = Q$ simultaneously.Thus,the condition $P^{\prime} = P$ and $Q^{\prime} = Q$ is impossible.Therefore,option $(C)$ is correct.

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?

Similar Questions

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

Two distributions $A$ and $B$ have the same mean. If their coefficients of variation are $6$ and $2$ respectively and $\sigma_A$ and $\sigma_B$ are their standard deviations,then:

The average marks of boys in a class is $40$ and that of girls is $45$. The average marks of both boys and girls combined is $42$. Then the percentage of boys in the class is (in $\%$)

Let the mean and variance of $12$ observations be $\frac{9}{2}$ and $4$ respectively. Later on,it was observed that two observations were considered as $9$ and $10$ instead of $7$ and $14$ respectively. If the correct variance is $\frac{m}{n}$,where $m$ and $n$ are co-prime,then $m + n$ is equal to

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module