In a group of students,the mean weight of boys is $65 \ kg$ and the mean weight of girls is $55 \ kg$. If the mean weight of all students is $61 \ kg$,what is the ratio of the number of boys to the number of girls in the group?

Let the mean and variance of four numbers $3, 7, x$ and $y$ $(x > y)$ be $5$ and $10$ respectively. Then the mean of four numbers $3+2x, 7+2y, x+y$ and $x-y$ is ..... .

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:

Let $X = \{11, 12, 13, \ldots, 40, 41\}$ and $Y = \{61, 62, 63, \ldots, 90, 91\}$ be two sets of observations. If $\bar{x}$ and $\bar{y}$ are their respective means and $\sigma^2$ is the variance of all the observations in $X \cup Y$,then $|\bar{x} + \bar{y} - \sigma^2|$ is equal to $.................$.

Let the mean and variance of $8$ numbers $-10, -7, -1, x, y, 9, 2, 16$ be $\frac{7}{2}$ and $\frac{293}{4}$ respectively. Then the mean of $4$ numbers $x, y, x + y + 1, |x - y|$ is:

If the sum of squares of the deviations from the mean of the data $x_i, (i=1, 2, \ldots, n)$ is $n\bar{x}^2$,where $\bar{x}$ is the mean of $x_i$'s,then the sum of squares of $x_i$'s is