The frequency distribution of daily working expenditure of families in a locality is as follows:

Expenditure in $Rs. (x)$	$0-50$	$50-100$	$100-150$	$150-200$	$200-250$
No. of families $(f)$	$24$	$33$	$37$	$b$	$25$

If the mode of the distribution is $Rs. 140$,then the value of $b$ is:

If both the mean and the standard deviation of $50$ observations $x_1, x_2, \ldots, x_{50}$ are equal to $16$,then the mean of $(x_1-5)^2, (x_2-5)^2, \ldots, (x_{50}-5)^2$ is

The range of the observations $20, 28, 40, 12, 30, 15, 50$ is $ . . . . . . $.

The mean and the standard deviation of $10$ observations are $20$ and $2$ respectively. Each of these $10$ observations is multiplied by $p$ and then reduced by $q$,where $p \neq 0$ and $q \neq 0$. If the new mean and new standard deviation (s.d.) become half of the original values,then $q$ is equal to

If the mean of the distribution is $2.6$,then the value of $y$ is:

Variate $x$	$1$	$2$	$3$	$4$	$5$
Freq $f$ of $x$	$4$	$5$	$y$	$1$	$2$

There are $60$ students in a class. The following is the frequency distribution of the marks obtained by the students in a test:
$\begin{array}{|l|l|l|l|l|l|l|} \hline \text{Marks} & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \text{Frequency} & x-2 & x & x^2 & (x+1)^2 & 2x & x+1 \\ \hline \end{array}$
where $x$ is a positive integer. Determine the mean and standard deviation of the marks.