The mean and variance of $5$ observations are $5$ and $8$ respectively. If $3$ observations are $1, 3, 5$,then the sum of cubes of the remaining two observations is

The class marks of a distribution are $6, 10, 14, 18, 22, 26, 30$. The class size is:

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

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 mean of the numbers $a, b, 8, 5, 10$ is $6$ and their variance is $6.8$. If $M$ is the mean deviation of the numbers about the mean,then $25M$ is equal to

Let $y_1, y_2, y_3, \dots, y_n$ be $n$ observations. Let $w_i = l y_i + k$ for all $i = 1, 2, 3, \dots, n$,where $l$ and $k$ are constants. If the mean of $y_i$ is $48$ and their standard deviation is $12$,and the mean of $w_i$ is $55$ and their standard deviation is $15$,then the values of $l$ and $k$ are: