Consider the frequency distribution of the given numbers. If the mean is known to be $3$,then the value of $f$ is:

Value	$1$	$2$	$3$	$4$
Frequency	$5$	$4$	$6$	$f$

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

The mean age of a combined group of men and women is $30$ years. If the means of the age of men and women are respectively $32$ and $27$,then the percentage of women in the group is

The mean and variance of a data of $10$ observations are $10$ and $2$, respectively. If an observation $\alpha$ in this data is replaced by $\beta$, then the mean and variance become $10.1$ and $1.99$, respectively. Then $\alpha + \beta$ equals.

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:

Consider the following statements:
$(1)$ Mode can be computed from a histogram.
$(2)$ Median is not independent of change of scale.
$(3)$ Variance is independent of change of origin and scale.
Which of these is/are correct?