(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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In a group of students,the mean weight of boys is $65 \ kg$ and the mean weight of girls is $55 \ kg$. If the mean weight of all students is $61 \ kg$,what is the ratio of the number of boys to the number of girls in the group?

Medium

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Let the median and the mean deviation about the median of $7$ observations $170, 125, 230, 190, 210, a, b$ be $170$ and $\frac{205}{7}$ respectively. Then the mean deviation about the mean of these $7$ observations is:

DifficultJEE MAIN 2024

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The mean and standard deviation of $40$ observations are $30$ and $5$ respectively. It was noticed that two of these observations $12$ and $10$ were wrongly recorded. If $\sigma$ is the standard deviation of the data after omitting the two wrong observations from the data,then $38 \sigma^{2}$ is equal to $.........$

DifficultJEE MAIN 2022

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If $M$ and $\sigma^2$ represent respectively the mean deviation from the mean and the variance for the data $1, 3, 5, 7, 11, 13, 17, 19, 23$,then $3(\sigma^2 - M) = $

MediumTS EAMCET 2023

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

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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$

In a group of students,the mean weight of boys is $65 \ kg$ and the mean weight of girls is $55 \ kg$. If the mean weight of all students is $61 \ kg$,what is the ratio of the number of boys to the number of girls in the group?

Let the median and the mean deviation about the median of $7$ observations $170, 125, 230, 190, 210, a, b$ be $170$ and $\frac{205}{7}$ respectively. Then the mean deviation about the mean of these $7$ observations is:

If $M$ and $\sigma^2$ represent respectively the mean deviation from the mean and the variance for the data $1, 3, 5, 7, 11, 13, 17, 19, 23$,then $3(\sigma^2 - M) = $

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