The mean of a set of $30$ observations is $75$. If each observation is multiplied by a non-zero number $\lambda$ and then each of them is decreased by $25$,their mean remains the same. The value of $\lambda$ is equal to

The mean of $5$ observations is $4.4$ and their variance is $8.24$. If three observations are $1, 2$ and $6$,the other two observations are

$A$ factory is operating in two shifts,day and night,with $70$ and $30$ workers respectively. If the per day mean wage of the day shift workers is $Rs. 54$ and the per day mean wage of all the workers is $Rs. 60$,then the per day mean wage of the night shift workers (in $Rs.$) is:

$\bar{x}$ and $\bar{y}$ are the arithmetic means of the runs of two batsmen $A$ and $B$ in $10$ innings respectively,and $\sigma_{A}$ and $\sigma_{B}$ are the standard deviations of their runs. If batsman $A$ is more consistent than $B$,then he is also a higher run scorer only when

Let $X = \{11, 12, 13, \ldots, 40, 41\}$ and $Y = \{61, 62, 63, \ldots, 90, 91\}$ be two sets of observations. If $\bar{x}$ and $\bar{y}$ are their respective means and $\sigma^2$ is the variance of all the observations in $X \cup Y$,then $|\bar{x} + \bar{y} - \sigma^2|$ is equal to $.................$.

The frequency distribution of the daily household expenditure of some families in a residential area is given below. If the mode of the distribution is $140$,what is the value of $b$?

Daily Expenditure (	$0-50$	$50-100$	$100-150$	$150-200$	$200-250$
Number of Families $(f)$	$24$	$33$	$37$	$b$	$25$