The mean and variance of a set of $15$ numbers are $12$ and $14$ respectively. The mean and variance of another set of $15$ numbers are $14$ and $\sigma^2$ respectively. If the variance of all the $30$ numbers in the two sets is $13$,then $\sigma^2$ is equal to $.........$.

Let $x_1, x_2,........,x_n$ be $n$ observations such that $\sum {{x_i}^2 = 300} $ and $\sum {{x_i} = 60} $ on value of $n$ among the following is

Let the mean and variance of the frequency distribution

be $6$ and $6.8$ respectively. If $x_{3}$ is changed from $8$ to $7 ,$ then the mean for the new data will be:

Let $r$ be the range and ${S^2} = \frac{1}{{n - 1}}\sum\limits_{i = 1}^n {{{({x_i} - \bar x)}^2}} $ be the $S.D.$ of a set of observations ${x_1},\,{x_2},\,.....{x_n}$, then

The average marks of $10$ students in a class was $60$ with a standard deviation $4$ , while the average marks of other ten students was $40$ with a standard deviation $6$ . If all the $20$ students are taken together, their standard deviation will be

If the variance of $10$ natural numbers $1,1,1, \ldots ., 1, k$ is less than $10 ,$ then the maximum possible value of $k$ is ...... .