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 $B$ $10$ $20$ $30$ $25$ $43$ $15$ $7$

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 -

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