Let one angle of a triangle be $60^{\circ}$. If the variance of the three angles of the triangle is $4614^{\circ}$,then the other two angles are

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 mean of the discrete distribution $8, 9, 6, 5, x, 4, 6, 5$ is $6$,then its standard deviation (nearest to two decimal places) is

If the standard deviation of the numbers $2, 3, 2x$,and $11$ is $3.5$,find the possible values of $x$.

If the mean of the data $7, 8, 9, 7, 8, 7, \lambda, 8$ is $8$,then the variance of the data is:

Let $x_1, x_2, x_3, \dots, x_n$ be $n$ observations,$\bar{x}$ be their arithmetic mean,and $\sigma^2$ be their variance.
Statement $-1$: The variance of observations $2x_1, 2x_2, 2x_3, \dots, 2x_n$ is $4\sigma^2$.
Statement $-2$: The arithmetic mean of $2x_1, 2x_2, 2x_3, \dots, 2x_n$ is $4\bar{x}$.