Let the mean and variance of $8$ numbers $x, y, 10, 12, 6, 12, 4, 8$ be $9$ and $9.25$ respectively. If $x > y$,then $3x - 2y$ is equal to $...........$.

For a group of $100$ students,the mean $\bar{x}_1$ and the standard deviation $\sigma_1$ of their marks were found to be $40$ and $15$ respectively. Later,it was observed that the scores $40$ and $50$ were misread as $30$ and $60$ respectively. If the mean and the standard deviation with the corrected observations of the scores are $\bar{x}_2$ and $\sigma_2$ respectively,then:

The mean of $n$ observations $x_{1}, x_{2}, \ldots, x_{n}$ is $\bar{x}$. If an observation $x_{q}$ is replaced by $x_{q}^{\prime}$, then the new mean is:

Consider the frequency distribution of the given numbers. If the mean is known to be $3$,then the value of $f$ is:

Value	$1$	$2$	$3$	$4$
Frequency	$5$	$4$	$6$	$f$

Let ${x_1}, {x_2}, ..., {x_n}$ be $n$ observations such that $\sum x_i^2 = 400$ and $\sum x_i = 80$. Then a possible value of $n$ among the following is:

The mean of $5$ observations is $4.4$ and the variance is $8.24$. If three of the five observations are $1, 2,$ and $6$,then the values of the other two observations are: