Let ${x_1}, {x_2}, ..., {x_n}$ be $n$ observations such that $\sum x_i^2 = 400$ and $\sum x_i = 80$. Then a possible value of $n$ among the following is:

If the mean and standard deviation ($S$.$D$.) of the data $3, 5, 7, a, b$ are $5$ and $2$ respectively,then $a$ and $b$ are the roots of the equation:

In a town, the probability that a sick person may need to be admitted to an $ICU$ is $10 \%$. If the probability that a person getting admitted to an $ICU$ goes above $5 \%$, then the threat level is raised. The minimum percentage of the population of the town that should fall sick in order to raise the threat level is

Statement $(I)$: The range of the ungrouped data does not change even if certain intermediate observations are removed.
Statement $(II)$: The value of the mean deviation of an ungrouped data about the median is always less than or equal to the value of the mean deviation computed about any other measure of central tendency.
Statement $(III)$: For a grouped data,range is approximated as the difference between the lower limit of the largest class and the upper limit of the smallest class.

For $(2n+1)$ observations ${x_1}, -{x_1}, {x_2}, -{x_2}, ....., {x_n}, -{x_n}$ and $0$,where all $x_i$ are distinct,let $S.D.$ and $M.D.$ denote the standard deviation and median respectively. Which of the following is always true?

The average marks of boys in a class is $52$ and that of girls is $42$. If the combined average of boys and girls is $50$,find the percentage of boys in the class.