The mean of a series $x_1, x_2, \dots, x_n$ is $\bar{X}$. If $x_2$ is replaced by $\lambda$,what will be the new mean?

Consider a set of $3n$ numbers having variance $4$. In this set,the mean of the first $2n$ numbers is $6$ and the mean of the remaining $n$ numbers is $3$. $A$ new set is constructed by adding $1$ to each of the first $2n$ numbers and subtracting $1$ from each of the remaining $n$ numbers. If the variance of the new set is $k$,then $9k$ is equal to .... .

For a frequency distribution,the $7^{th}$ decile is computed by the formula:

For $(2n+1)$ observations ${x_1}, -{x_1}, {x_2}, -{x_2}, ....., {x_n}, -{x_n}$ and $0$,where all $x_i$ are distinct,let $S.D.$ and $M.D.$ denote the standard deviation and median respectively. Which of the following is always true?

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.

The mean and variance of $7$ observations are $8$ and $16$ respectively. If the first five observations are $2, 4, 10, 12, 14$,then the absolute difference of the remaining two observations is