(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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While calculating the mean and variance of $10$ readings,a student wrongly used the reading $52$ for the correct reading $25$. He obtained the mean and variance as $45$ and $16$ respectively. Find the correct mean and the variance.

Difficult

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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 $25$ teachers in a school is $40 \text{ years}$. $A$ teacher retires at the age of $60 \text{ years}$ and a new teacher is appointed in his place. If now the mean age of the teachers in this school is $39 \text{ years}$,then the age (in years) of the newly appointed teacher is

MediumJEE MAIN 2017

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Let $n \geq 3$. $A$ list of numbers $0 < x_1 < x_2 < \ldots < x_n$ has mean $\mu$ and standard deviation $\sigma$. $A$ new list of numbers is formed as follows: $y_1=0, y_2=x_2, \ldots, y_{n-1}=x_{n-1}, y_n=x_1+x_n$. The mean and the standard deviation of the new list are $\hat{\mu}$ and $\hat{\sigma}$. Which of the following is necessarily true?

DifficultKVPY 2013

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If the mean and variance of six observations $7, 10, 11, 15, a, b$ are $10$ and $\frac{20}{3}$ respectively,then the value of $|a-b|$ is equal to:

MediumJEE MAIN 2021

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While calculating the mean and variance of $10$ readings,a student wrongly used the reading $52$ for the correct reading $25$. He obtained the mean and variance as $45$ and $16$ respectively. Find the correct mean and the variance.

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 $25$ teachers in a school is $40 \text{ years}$. $A$ teacher retires at the age of $60 \text{ years}$ and a new teacher is appointed in his place. If now the mean age of the teachers in this school is $39 \text{ years}$,then the age (in years) of the newly appointed teacher is

If the mean and variance of six observations $7, 10, 11, 15, a, b$ are $10$ and $\frac{20}{3}$ respectively,then the value of $|a-b|$ is equal to:

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