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 average weight of students in a class of $35$ students is $40 \ kg$. If the weight of the teacher is included,the average weight increases by $0.5 \ kg$. The weight of the teacher is.....$kg$.

If $\alpha$ and $\beta$ are respectively the mean deviation about the mean and the variance of the first five prime numbers,then the ordered pair $(\alpha, \beta)$ is:

Two data sets each of size $5$ are given. If the variances are $4$ and $5$ and their corresponding means are $2$ and $4$ respectively,then what is the variance of the combined data set?

The mean of five observations is $4$ and their variance is $5.2$. If three of these observations are $1, 2$ and $6$,then the other two are

Let $x_1, x_2, \ldots, x_{11}$ be the observations satisfying $\sum_{i=1}^{11}(x_i-4)=22$ and $\sum_{i=1}^{11}(x_i-4)^2=154$. If the mean and variance of the observations are $\alpha$ and $\beta$,then the quadratic equation having the roots $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$ is