The mean of the numbers $a, b, 8, 5, 10$ is $6$ and the variance is $6.8$. Then which of the following gives possible values of $a$ and $b$?

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 ..... .

The mean life of a sample of $60$ bulbs was $650$ hours and the standard deviation was $8$ hours. $A$ second sample of $80$ bulbs has a mean life of $660$ hours and standard deviation $7$ hours. Find the overall standard deviation.

Two distributions $A$ and $B$ have the same mean. If their coefficients of variation are $6$ and $2$ respectively and $\sigma_A$ and $\sigma_B$ are their standard deviations,then:

If $65$ is the range of the ungrouped data $50, 70, 60, B, 20, 40$,then the absolute difference of the possible values of $B$ 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