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

The average incomes of the people in two villages are $P$ and $Q$,respectively. Assume that $P \neq Q$. $A$ person moves from the first village to the second village. The new average incomes are $P^{\prime}$ and $Q^{\prime}$,respectively. Which of the following is not possible?

If the mean of the distribution is $2.6$,then the value of $y$ is:

Variate $x$	$1$	$2$	$3$	$4$	$5$
Freq $f$ of $x$	$4$	$5$	$y$	$1$	$2$

If the mean and standard deviation ($S$.$D$.) of the data $3, 5, 7, a, b$ are $5$ and $2$ respectively,then $a$ and $b$ are the roots of the equation:

The mean and standard deviation of $20$ observations are found to be $10$ and $2$ respectively. On rechecking,it was found that an observation $8$ was incorrect. Calculate the correct mean and standard deviation if the wrong item is omitted.

The mean and standard deviation of $100$ observations are $40$ and $5.1$,respectively. By mistake,one observation is taken as $50$ instead of $40$. If the correct mean and the correct standard deviation are $\mu$ and $\sigma$ respectively,then $10(\mu+\sigma)$ is equal to