If mean and variance of data 65,68,58,44 , 48,45,60, α, β, 60 where α>β are 56 and 66.2 respe

English

Gujarati

Hindi

13.Statistics

medium

If the mean and variance of the data $65,68,58,44$, $48,45,60, \alpha, \beta, 60$ where $\alpha>\beta$ are $56$ and $66.2$ respectively, then $\alpha^2+\beta^2$ is equal to

A

$6435$

B

$6798$

C

$6344$

D

$4312$

(JEE MAIN-2024)

Solution

$ \overline{\mathrm{x}}=56 $

$ \sigma^2=66.2 $

$ \Rightarrow \frac{\alpha^2+\beta^2+25678}{10}-(56)^2=66.2 $

$ \therefore \alpha^2+\beta^2=6344$

Standard 11

Mathematics

Share

Similar Questions

The mean and standard deviation of $15$ observations are found to be $8$ and $3$ respectively. On rechecking it was found that, in the observations, $20$ was misread as $5$ . Then, the correct variance is equal to……

medium

(JEE MAIN-2022)

Calculate the mean, variance and standard deviation for the following distribution:

Class $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ $80-90$ $90-100$

$f_i$ $3$ $7$ $12$ $15$ $8$ $3$ $2$

hard

Let $\mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathrm{N}$ and $\mathrm{a}<\mathrm{b}<\mathrm{c}$. Let the mean, the mean deviation about the mean and the variance of the $5$ observations $9$,$25$, $a$, $b$, $c$ be $18$,$4$ and $\frac{136}{5}$, respectively. Then $2 \mathrm{a}+\mathrm{b}-\mathrm{c}$ is equal to …………..

hard

(JEE MAIN-2024)

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

medium

If the mean and variance of the frequency distribution

$x_i$ $2$ $4$ $6$ $8$ $10$ $12$ $14$ $16$

$f_i$ $4$ $4$ $\alpha$ $15$ $8$ $\beta$ $4$ $5$

are $9$ and $15.08$ respectively, then the value of $\alpha^2+\beta^2-\alpha \beta$ is $…………$.

hard

(JEE MAIN-2023)