(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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The mean of the following frequency distribution is $50$ and $\Sigma f = 120$. Find the missing frequencies $f_1$ and $f_2$.
Class $0-20$ $20-40$ $40-60$ $60-80$ $80-100$
$f$ $17$ $f_1$ $32$ $f_2$ $19$

Medium

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Let $a, b \in R$. Let the mean and the variance of $6$ observations $-3, 4, 7, -6, a, b$ be $2$ and $23$,respectively. The mean deviation about the mean of these $6$ observations is:

MediumJEE MAIN 2024

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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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Let the mean and standard deviation of marks of class $A$ of $100$ students be respectively $40$ and $\alpha ( > 0)$,and the mean and standard deviation of marks of class $B$ of $n$ students be respectively $55$ and $30-\alpha$. If the mean and variance of the marks of the combined class of $100+n$ students are respectively $50$ and $350$,then the sum of variances of classes $A$ and $B$ is:

DifficultJEE MAIN 2023

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If the mean of two samples of sizes $20$ and $30$ are $25$ and $10$ respectively,and their variances are $9$ and $16$ respectively,then their combined variance is:

MediumAP EAMCET 2020

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Class	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$
$f$	$17$	$f_1$	$32$	$f_2$	$19$

Similar Questions

The mean of the following frequency distribution is $50$ and $\Sigma f = 120$. Find the missing frequencies $f_1$ and $f_2$.Class$0-20$$20-40$$40-60$$60-80$$80-100$$f$$17$$f_1$$32$$f_2$$19$

Let $a, b \in R$. Let the mean and the variance of $6$ observations $-3, 4, 7, -6, a, b$ be $2$ and $23$,respectively. The mean deviation about the mean of these $6$ observations is:

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

If the mean of two samples of sizes $20$ and $30$ are $25$ and $10$ respectively,and their variances are $9$ and $16$ respectively,then their combined variance is:

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The mean of the following frequency distribution is $50$ and $\Sigma f = 120$. Find the missing frequencies $f_1$ and $f_2$.
Class $0-20$ $20-40$ $40-60$ $60-80$ $80-100$
$f$ $17$ $f_1$ $32$ $f_2$ $19$