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 age of $25$ teachers in a school is $40$ years. $A$ teacher retires at the age of $60$ years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is $39$ years,then the age (in years) of the newly appointed teacher is..........

Let the mean and standard deviation of marks of class $A$ of $100$ students be respectively $40$ and $\alpha ( > 0)$,and the mean and standard deviation of marks of class $B$ of $n$ students be respectively $55$ and $30-\alpha$. If the mean and variance of the marks of the combined class of $100+n$ students are respectively $50$ and $350$,then the sum of variances of classes $A$ and $B$ is:

Let $a$ and $b$ be two real numbers. If the arithmetic mean and the variance of $a, b, 8, 5$ and $10$ are respectively $6$ and $6.8$,then an ordered pair $(a, b) =$

The mean and variance of $n$ observations are $8$ and $16$, respectively. If the sum of the first $(n - 1)$ observations is $48$ and the sum of squares of the first $(n - 1)$ observations is $496$, then the value of $n$ is:

The mean and standard deviation of $50$ observations are $15$ and $2$ respectively. It was found that one incorrect observation was taken such that the sum of the correct and incorrect observations is $70$. If the correct mean is $16$,then the correct variance is equal to