If $x_1, x_2, \ldots, x_n$ are $n$ observations such that $\sum_{i=1}^n x_i^2 = 400$ and $\sum_{i=1}^n x_i = 80$,then the least value of $n$ is

The mean and variance of a set of $6$ terms are $11$ and $24$ respectively,and the mean and variance of another set of $3$ terms are $14$ and $36$ respectively. Then,the variance of all $9$ terms is equal to:

The mean and variance of $5$ observations are $5$ and $8$ respectively. If $3$ observations are $1, 3, 5$,then the sum of cubes of the remaining two observations is

In a set of $2n$ distinct observations,each of the observations below the median is increased by $5$ and each of the remaining observations is decreased by $3$. Then the mean of the new set of observations

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:

$A$ set of four observations has mean $1$ and variance $13$. Another set of six observations has mean $2$ and variance $1$. Then,the variance of all these $10$ observations is equal to: