(B) Let $S_1$ be the total income of the first group (salary $ ₹ 10,000$).Giv

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(B) Let $S_1$ be the total income of the first group (salary $ ₹ 10,000$).Given that $S_1 Let $N_1$ and $N_2$ be the number of people in the first and second groups,respectively.The initial total income is $S_{total} = S_1 + S_2$.The new total income after the changes is $S'_{total} = S_1(1 + 0.05) + S_2(1 - 0.05) = 1.05 S_1 + 0.95 S_2$.The change in total income is $\Delta S = S'_{total} - S_{total} = (1.05 S_1 + 0.95 S_2) - (S_1 + S_2) = 0.05 S_1 - 0.05 S_2 = 0.05(S_1 - S_2)$.Since $S_1 Therefore,the total income decreases,and consequently,the average income of all people decreases.

Class 11 Mathematics Statistics Word problem -Statistics

In a city,the total income of all people with a salary below $₹ 10,000$ per annum is less than the total income of all people with a salary above $₹ 10,000$ per annum. If the salaries of people in the first group increase by $5 \%$ and the salaries of people in the second group decrease by $5 \%$,then the average income of all people:

KVPY 2013 All KVPY

A
increases
B
decreases
C
remains the same
D
cannot be determined from the data

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

JEE MAIN 2022

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The mean age of a combined group of men and women is $30$ years. If the means of the age of men and women are respectively $32$ and $27$,then the percentage of women in the group is

Medium

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The expenditure of a family for a certain month were as follows:
Food - Rs. $560$,Rent - Rs. $420$,Clothes - Rs. $180$,Education - Rs. $160$,Other items - Rs. $120$
$A$ pie graph representing this data would show the expenditure for clothes by a sector whose angle equals......$^o$

Difficult

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The mean of $5$ observations is $4.4$ and the variance is $8.24$. If three of the five observations are $1, 2,$ and $6$,then the values of the other two observations are:

EasyMHT CET 2022

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If the mean of the data:
Class $5 - 10$ $10 - 15$ $15 - 20$ $20 - 25$ $25 - 30$ $30 - 35$
Frequency $2$ $k$ $28$ $54$ $k + 1$ $5$

is $21$, then $k$ is one of the roots of the equation:

DifficultJEE MAIN 2026

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Class	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$
Frequency	$2$	$k$	$28$	$54$	$k + 1$	$5$

Similar Questions

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

The mean age of a combined group of men and women is $30$ years. If the means of the age of men and women are respectively $32$ and $27$,then the percentage of women in the group is

The expenditure of a family for a certain month were as follows:Food - Rs. $560$,Rent - Rs. $420$,Clothes - Rs. $180$,Education - Rs. $160$,Other items - Rs. $120$$A$ pie graph representing this data would show the expenditure for clothes by a sector whose angle equals......$^o$

The mean of $5$ observations is $4.4$ and the variance is $8.24$. If three of the five observations are $1, 2,$ and $6$,then the values of the other two observations are:

If the mean of the data:Class$5 - 10$$10 - 15$$15 - 20$$20 - 25$$25 - 30$$30 - 35$Frequency$2$$k$$28$$54$$k + 1$$5$is $21$, then $k$ is one of the roots of the equation:

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The expenditure of a family for a certain month were as follows:
Food - Rs. $560$,Rent - Rs. $420$,Clothes - Rs. $180$,Education - Rs. $160$,Other items - Rs. $120$
$A$ pie graph representing this data would show the expenditure for clothes by a sector whose angle equals......$^o$

If the mean of the data:
Class $5 - 10$ $10 - 15$ $15 - 20$ $20 - 25$ $25 - 30$ $30 - 35$
Frequency $2$ $k$ $28$ $54$ $k + 1$ $5$

is $21$, then $k$ is one of the roots of the equation: