The average age of a group of men and women is $30$ years. If the average age of men is $32$ years and that of women is $27$ years,what is the percentage of women in the group?

Suppose a class has $7$ students. The average marks of these students in the mathematics examination is $62$,and their variance is $20$. $A$ student fails in the examination if they get less than $50$ marks. In the worst-case scenario,what is the maximum number of students who can fail?

If $65$ is the range of the ungrouped data $50, 70, 60, B, 20, 40$,then the absolute difference of the possible values of $B$ is

If the mean and the variance of $6, 4, a, 8, b, 12, 10, 13$ are $9$ and $9.25$ respectively,then $a+b+ab$ is equal to:

$A$ market with $3900$ operating firms has the following distribution for firms arranged according to various income groups of workers. If a histogram for the above distribution is constructed,the highest bar in the histogram would correspond to the class:

Income group	No. of firms
$150-300$	$300$
$300-500$	$500$
$500-800$	$900$
$800-1200$	$1000$
$1200-1800$	$1200$

The weighted mean of the first $n$ natural numbers,where the weights are equal to the squares of the corresponding numbers,is: