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

The $A.M.$ of $n$ observations is $M$. If the sum of $n - 4$ observations is $a$,then the mean of the remaining $4$ observations is:

Let $a$ and $b$ be two real numbers. If the arithmetic mean and the variance of $a, b, 8, 5$ and $10$ are respectively $6$ and $6.8$,then an ordered pair $(a, b) =$

The mean and the standard deviation of $10$ observations are $20$ and $2$ respectively. Each of these $10$ observations is multiplied by $p$ and then reduced by $q$,where $p \neq 0$ and $q \neq 0$. If the new mean and new standard deviation (s.d.) become half of the original values,then $q$ is equal to

If both the mean and the standard deviation of $50$ observations $x_1, x_2, \ldots, x_{50}$ are equal to $16$,then the mean of $(x_1-5)^2, (x_2-5)^2, \ldots, (x_{50}-5)^2$ is

Find the least positive value of $k$,if the range of $15, 14, k, 25, 30, 35$ is $23$.