The mean and variance of six observations are $6$ and $12$ respectively. If each observation is multiplied by $3$,then the new variance of the resulting observations is:

If each observation of a distribution with standard deviation $\sigma$ is increased by $\lambda$,find the variance of the new observations.

The standard deviations of $x_i (i=1, 2, \ldots, 10)$ and $y_i (i=1, 2, \ldots, 10)$ are $a$ and $b$ respectively. $\bar{x}$ and $\bar{y}$ are the means of these two sets of observations. If $z_i = (x_i - \bar{x})(y_i - \bar{y})$ and $\sum_{i=1}^{10} z_i = c$,then the standard deviation of the observations $(x_i - y_i)$ for $i=1, 2, \ldots, 10$ is:

From the data given below,state which group is more variable,$A$ or $B$?

Marks	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Group $A$	$9$	$17$	$32$	$33$	$40$	$10$	$9$
Group $B$	$10$	$20$	$30$	$25$	$43$	$15$	$7$

The following table shows the marks obtained by two students,Ravi and Hashina,in $10$ tests (out of $100$ marks each).

Student	Marks
Ravi	$25, 50, 45, 30, 70, 42, 36, 48, 35, 60$
Hashina	$10, 70, 50, 20, 95, 55, 42, 60, 48, 80$

Who is more intelligent and who is more consistent?

The mean and variance of $10$ observations were calculated as $15$ and $15$ respectively by a student who took by mistake $25$ instead of $15$ for one observation. Then,the correct standard deviation is $.....$