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

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 $………$.

The variance $\sigma^2$ of the data is $ . . . . . .$

A data consists of $n$ observations

${x_1},{x_2},……,{x_n}.$ If $\sum\limits_{i – 1}^n {{{({x_i} + 1)}^2}}  = 9n$ and $\sum\limits_{i – 1}^n {{{({x_i} – 1)}^2}}  = 5n,$ then the standard deviation of this data is

The mean and standard deviation of some data for the time taken to complete . a test are calculated with the following results:

Number of observations $=25,$ mean $=18.2$ seconds, standard deviation $=3.25 s$

Further, another set of 15 observations $x_{1}, x_{2}, \ldots, x_{15},$ also in seconds, is now available and we have $\sum_{i=1}^{15} x_{i}=279$ and $\sum_{i=1}^{15} x_{i}^{2}=5524 .$ Calculate the standard deviation based on all 40 observations.