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

The mean of $100$ observations is $45$. It was later found that two observations $19$ and $31$ were incorrectly recorded as $91$ and $13$. The correct mean is...

If the mean of two samples of sizes $20$ and $30$ are $25$ and $10$ respectively,and their variances are $9$ and $16$ respectively,then their combined variance is:

If the coefficient of variation is $ 60 $ and the standard deviation is $ 24 $,then the arithmetic mean is:

If for some $x \in R^{+} \cup \{0\}$,the frequency distribution of the marks obtained by $20$ students in a test is given by the table below,then find the mean of the marks.

Marks:	$2$	$3$	$5$	$7$
Frequency:	$(x+1)^2$	$2x-5$	$x^2-3x$	$x$

$A$ 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: