If the median and the range of four numbers $\{x, y, 2x + y, x - y\}$,where $0 < y < x < 2y$,are $10$ and $28$ respectively,then the mean of the numbers is

Let $y_1, y_2, y_3, \dots, y_n$ be $n$ observations. Let $w_i = l y_i + k$ for all $i = 1, 2, 3, \dots, n$,where $l$ and $k$ are constants. If the mean of $y_i$ is $48$ and their standard deviation is $12$,and the mean of $w_i$ is $55$ and their standard deviation is $15$,then the values of $l$ and $k$ are:

In a city,the total income of all people with a salary below $₹ 10,000$ per annum is less than the total income of all people with a salary above $₹ 10,000$ per annum. If the salaries of people in the first group increase by $5 \%$ and the salaries of people in the second group decrease by $5 \%$,then the average income of all people:

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?

The number of values of $a \in N$ such that the variance of $3, 7, 12, a, 43-a$ is a natural number is (Mean $= 13$).

Marks obtained by all the students of class $12$ are presented in a frequency distribution with classes of equal width. Let the median of this grouped data be $14$ with median class interval $12-18$ and median class frequency $12$. If the number of students whose marks are less than $12$ is $18$,then the total number of students is