The mean and variance of the marks obtained by the students in a test are $10$ and $4$ respectively. Later, the marks of one of the students is increased from $8$ to $12$ . If the new mean of the marks is $10.2.$ then their new variance is equal to :
The mean and variance of the marks obtained by the students in a test are $10$ and $4$ respectively. Later, the marks of one of the students is increased from $8$ to $12$ . If the new mean of the marks is $10.2.$ then their new variance is equal to :
- [JEE MAIN 2023]
- A
$4.04$
- B
$4.08$
- C
$3.96$
- D
$3.92$
Similar Questions
From the data given below state which group is more variable, $A$ or $B$ ?
Marks
$10-20$
$20-30$
$30-40$
$40-50$
$50-60$
$60-70$
$70-80$
Group $A$
$9$
$17$
$32$
$33$
$40$
$10$
$9$
Group $B$
$10$
$20$
$30$
$25$
$43$
$15$
$7$
From the data given below state which group is more variable, $A$ or $B$ ?
| Marks | $10-20$ | $20-30$ | $30-40$ | $40-50$ | $50-60$ | $60-70$ | $70-80$ |
| Group $A$ | $9$ | $17$ | $32$ | $33$ | $40$ | $10$ | $9$ |
| Group $B$ | $10$ | $20$ | $30$ | $25$ | $43$ | $15$ | $7$ |
The mean and standard deviation of $15$ observations were found to be $12$ and $3$ respectively. On rechecking it was found that an observation was read as $10$ in place of $12$ . If $\mu$ and $\sigma^2$ denote the mean and variance of the correct observations respectively, then $15\left(\mu+\mu^2+\sigma^2\right)$ is equal to$...................$
The mean and standard deviation of $15$ observations were found to be $12$ and $3$ respectively. On rechecking it was found that an observation was read as $10$ in place of $12$ . If $\mu$ and $\sigma^2$ denote the mean and variance of the correct observations respectively, then $15\left(\mu+\mu^2+\sigma^2\right)$ is equal to$...................$
- [JEE MAIN 2024]
The variance of $10$ observations is $16$. If each observation is doubled, then standard deviation of new data will be -
The variance of $10$ observations is $16$. If each observation is doubled, then standard deviation of new data will be -
Mean of $5$ observations is $7.$ If four of these observations are $6, 7, 8, 10$ and one is missing then the variance of all the five observations is
Mean of $5$ observations is $7.$ If four of these observations are $6, 7, 8, 10$ and one is missing then the variance of all the five observations is
- [JEE MAIN 2013]
The average marks of $10$ students in a class was $60$ with a standard deviation $4$, while the average marks of other ten students was $40$ with a standard deviation $6$. If all the $20$ students are taken together, their standard deviation will be
The average marks of $10$ students in a class was $60$ with a standard deviation $4$, while the average marks of other ten students was $40$ with a standard deviation $6$. If all the $20$ students are taken together, their standard deviation will be