The mean and variance of seven observations are $8$ and $16$,respectively. If $5$ of the observations are $2, 4, 10, 12, 14$,then the product of the remaining two observations is

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?

Find the least positive value of $k$,if the range of $15, 14, k, 25, 30, 35$ is $23$.

Mean and standard deviation of $100$ observations were found to be $40$ and $10$,respectively. If at the time of calculation,two observations were wrongly taken as $30$ and $70$ in place of $3$ and $27$ respectively,find the correct standard deviation.

The coefficients of variation of two distributions are $60$ and $70$. The standard deviations are $21$ and $16$ respectively. Find their means.

An online exam is attempted by $50$ candidates,out of which $20$ are boys. The average marks obtained by boys is $12$ with a variance of $2$. The variance of marks obtained by $30$ girls is also $2$. The average marks of all $50$ candidates is $15$. If $\mu$ is the average marks of girls and $\sigma^{2}$ is the variance of marks of $50$ candidates,then $\mu+\sigma^{2}$ is equal to ...... .