The mean marks of $25$ boys in a class is $61$ and the mean marks of $35$ girls in the same class is $58$. Then,the mean of all $60$ students is (in $.25$)

An online exam is attempted by $50$ candidates,out of which $20$ are boys. The average marks obtained by boys is $12$ with a variance of $2$. The variance of marks obtained by $30$ girls is also $2$. The average marks of all $50$ candidates is $15$. If $\mu$ is the average marks of girls and $\sigma^{2}$ is the variance of marks of $50$ candidates,then $\mu+\sigma^{2}$ is equal to ...... .

The mean and variance of $7$ observations are $8$ and $16$ respectively. If five of the observations are $2, 4, 10, 12, 14$,find the remaining two observations.

The mean of $100$ observations is $45$. It was later found that two observations $19$ and $31$ were incorrectly recorded as $91$ and $13$. The correct mean is...

The mean and variance of the marks obtained by $n$ 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:

If the algebraic sum of deviations of $20$ observations from $30$ is $20$,then the mean of the observations is: