The mean and variance of $7$ observations are $8$ and $16$ respectively. If one observation $14$ is omitted and $a$ and $b$ are respectively the mean and variance of the remaining $6$ observations,then $a+3b-5$ 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 $15(\mu+\mu^2+\sigma^2)$ is equal to $...................$

If $M$ and $\sigma^2$ represent respectively the mean deviation from the mean and the variance for the data $1, 3, 5, 7, 11, 13, 17, 19, 23$,then $3(\sigma^2 - M) = $

$A$ $100$ mark examination was administered to a class of $50$ students. Despite only integer marks being given,the average score of the class was $47.5$. The maximum number of students who could have received marks greater than the class average is:

Integers $1, 2, 3, \ldots, n$ $(n \geq 3)$ are written on a blackboard and an integer $k$ $(1 < k < n)$ is erased. The average of the remaining numbers is $16$. Then $n + k$ is

If the coefficient of variation is $ 60 $ and the standard deviation is $ 24 $,then the arithmetic mean is: