The mean of a data set consisting of $20$ observations is $40$. If one observation $53$ was wrongly recorded as $33$,then the correct mean will be

If the mean of the following frequency distribution is $2.6$,find the value of $f$.

$x_i$	$1$	$2$	$3$	$4$	$5$
$f_i$	$5$	$4$	$f$	$2$	$3$

In a Mathematics test,the average marks of boys is $x \%$ and the average marks of girls is $y \%$ with $x \neq y$. If the average marks of all students is $z \%$,the ratio of the number of girls to the total number of students is

Consider a set of $3n$ numbers having variance $4$. In this set,the mean of the first $2n$ numbers is $6$ and the mean of the remaining $n$ numbers is $3$. $A$ new set is constructed by adding $1$ to each of the first $2n$ numbers and subtracting $1$ from each of the remaining $n$ numbers. If the variance of the new set is $k$,then $9k$ is equal to .... .

Let $\bar{x}, M$ and $\sigma^2$ be respectively the mean,mode and variance of $n$ observations $x_1, x_2, ..., x_n$ and $d_i = -x_i - a, i = 1, 2, ..., n$,where $a$ is any number. Statement $I$: Variance of $d_1, d_2, ..., d_n$ is $\sigma^2$. Statement $II$: Mean and mode of $d_1, d_2, ..., d_n$ are $-\bar{x} - a$ and $-M - a$,respectively.

The mean and variance of the data $4, 5, 6, 6, 7, 8, x, y$ where $x < y$ are $6$ and $\frac{9}{4}$ respectively. Then $x^{4} + y^{2}$ is equal to