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.

Let $a, b, c \in N$ and $a < b < c$. Let the mean,the mean deviation about the mean,and the variance of the $5$ observations $9, 25, a, b, c$ be $18, 4$,and $\frac{136}{5}$,respectively. Then $2a + b - c$ is equal to:

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 $.25$)

The average age of a group of men and women is $30$ years. If the average age of men is $32$ years and that of women is $27$ years,what is the percentage of women in the group?

The mean and standard deviation of a set of $n_{1}$ observations are $\bar{x}_{1}$ and $s_{1},$ respectively,while the mean and standard deviation of another set of $n_{2}$ observations are $\bar{x}_{2}$ and $s_{2},$ respectively. Show that the standard deviation of the combined set of $(n_{1}+n_{2})$ observations is given by $SD = \sqrt{\frac{n_{1}(s_{1})^{2}+n_{2}(s_{2})^{2}}{n_{1}+n_{2}}+\frac{n_{1} n_{2}(\bar{x}_{1}-\bar{x}_{2})^{2}}{(n_{1}+n_{2})^{2}}}$.

Let the median and the mean deviation about the median of $7$ observations $170, 125, 230, 190, 210, a, b$ be $170$ and $\frac{205}{7}$ respectively. Then the mean deviation about the mean of these $7$ observations is: