Let $r$ be the range and $S^2 = \frac{1}{n - 1} \sum_{i = 1}^n (x_i - \bar{x})^2$ be the variance of a set of observations $x_1, x_2, \dots, x_n$. Then:

The mean and standard deviation of a group of $100$ observations were found to be $20$ and $3$,respectively. Later on,it was found that three observations were incorrect,which were recorded as $21, 21,$ and $18$. Find the mean and standard deviation if the incorrect observations are omitted.

For two data sets,each of size $5$,the variances are given to be $4$ and $5$ and the corresponding means are given to be $2$ and $4$,respectively. The variance of the combined data set is

Suppose that the mean and median of the non-negative numbers $21, 8, 17, a, 51, 103, b, 13, 67$ $(a > b)$ are $40$ and $21$, respectively. If the mean deviation about the median is $26$, then $2a$ is equal to:

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

Consider the following data:

Daily wage (Rs.)	$30$-$40$	$40$-$50$	$50$-$60$	$60$-$70$	$70$-$80$	$80$-$90$
No. of workers	$17$	$28$	$21$	$15$	$13$	$6$

The coefficient of variation of the above distribution of wages,if its standard deviation is $14.72$,is