The mean of $n$ values of a distribution is $\bar{x}$. If the first value is increased by $1$,the second value by $2$,and so on,what will be the mean of the new values?

If the sum of the deviations of $50$ observations from $30$ is $50$,then the mean of these observations is:

The first of the two samples in a group has $100$ items with mean $15$ and standard deviation $3$. If the whole group has $250$ items with mean $15.6$ and standard deviation $\sqrt{13.44}$,then the standard deviation of the second sample is:

The mean and the standard deviation of $10$ observations are $20$ and $2$ respectively. Each of these $10$ observations is multiplied by $p$ and then reduced by $q$,where $p \neq 0$ and $q \neq 0$. If the new mean and new standard deviation (s.d.) become half of the original values,then $q$ is equal to

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 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?