Let mean and variance of four numbers 3,7, x and y(x>y) be 5 and 10 respectively. Then mean of fo

English

Gujarati

Hindi

13.Statistics

hard

Let the mean and variance of four numbers $3,7, x$ and $y(x>y)$ be $5$ and $10$ respectively. Then the mean of four numbers $3+2 \mathrm{x}, 7+2 \mathrm{y}, \mathrm{x}+\mathrm{y}$ and $x-y$ is ..... .

A

$10$

B

$11$

C

$12$

D

$48$

(JEE MAIN-2021)

Solution

$5=\frac{3+7+x+y}{4} \Rightarrow x+y=10$

$\operatorname{Var}(x)=10=\frac{3^{2}+7^{2}+x^{2}+y^{2}}{4}-25$

$140=49+9+x^{2}+y^{2}$

$x^{2}+y^{2}=82$

$x+y=10$

$\Rightarrow(x, y)=(9,1)$

Four numbers are $21,9,10,8$

$\text { Mean }=\frac{48}{4}=12$

Standard 11

Mathematics

Share

Similar Questions

Mean and standard deviation of 100 observations were found to be 40 and 10 , respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively, find the correct standard deviation.

hard

If the mean of the frequency distribution

Class: $0-10$ $10-20$ $20-30$ $30-40$ $40-50$

Frequency $2$ $3$ $x$ $5$ $4$

is $28$ , then its variance is $……..$.

hard

(JEE MAIN-2023)

Let $x_1, x_2, x_3, x_4, ………. , x_n$ be $n$ observations and let $\bar x$ be their arithmetic mean and $\sigma ^2$ be their variance.

Statement $-1$ : Variance of observations $2x_1, 2x_2, 2x_3, ……, 2x_n$ is $4\sigma ^2$ .

Statement $-2$ : Arithmetic mean of $2x _1, 2x_2, 2x_3, ……, 2x_n$ is $4\bar x$ .

normal

The standard deviation of $25$ numbers is $40$. If each of the numbers is increased by $5$, then the new standard deviation will be

easy

Find the standard deviation for the following data:

${x_i}$ $3$ $8$ $13$ $18$ $25$

${f_i}$ $7$ $10$ $15$ $10$ $6$

medium