If each observation of a raw data whose variance is $\sigma^2$ is multiplied by $\lambda$,then the variance of the new set is

Find the mean,variance,and standard deviation using the short-cut method for the following data:

Height in cms	$70-75$	$75-80$	$80-85$	$85-90$	$90-95$	$95-100$	$100-105$	$105-110$	$110-115$
No. of children	$3$	$4$	$7$	$7$	$15$	$9$	$6$	$6$	$3$

If the variance of the following frequency distribution is $50$,then $x$ is equal to:

Class	$10-20, 20-30, 30-40$
Frequency	$2, x, 2$

The variance of the first $10$ natural numbers which are multiples of $3$ is

Find the variance of the sequence $a, a + d, a + 2d, \dots, a + 2nd$.

The mean of a set of $10$ observations is $5$ and the standard deviation is $2\sqrt{6}$. If the mean of another set of $20$ observations is $5$ and the standard deviation is $3\sqrt{2}$,what is the standard deviation of the combined set of $30$ observations?