The mean and the variance of five observations are $4$ and $5.20,$ respectively. If three of the observations are $3, 4,$ and $4,$ then the absolute value of the difference of the other two observations is

Marks obtained by all the students of class $12$ are presented in a frequency distribution with classes of equal width. Let the median of this grouped data be $14$ with median class interval $12-18$ and median class frequency $12$. If the number of students whose marks are less than $12$ is $18$,then the total number of students is

The weighted mean of the first $n$ natural numbers,where the weights are equal to the squares of the corresponding numbers,is:

An analysis of monthly wages paid to workers in two firms $A$ and $B$,belonging to the same industry,gives the following results:

\text{Parameter}	\text{Firm } $A$ \text{ and Firm } $B$
\text{No. of wage earners}	$A: 586, B: 648$
\text{Mean of monthly wages}	$Rs. 5253$
\text{Variance of wages}	$A: 100, B: 121$

Which firm,$A$ or $B$,pays a larger total amount as monthly wages?

The mean and standard deviation of $50$ observations are $15$ and $2$ respectively. It was found that one incorrect observation was taken such that the sum of the correct and incorrect observations is $70$. If the correct mean is $16$,then the correct variance is equal to

If the mean and variance of six observations $7, 10, 11, 15, a, b$ are $10$ and $\frac{20}{3}$ respectively,then the value of $|a-b|$ is equal to: