The number of values of $a \in N$ such that the variance of $3, 7, 12, a, 43-a$ is a natural number is (Mean $= 13$).

Let the mean and standard deviation of marks of class $A$ of $100$ students be respectively $40$ and $\alpha ( > 0)$,and the mean and standard deviation of marks of class $B$ of $n$ students be respectively $55$ and $30-\alpha$. If the mean and variance of the marks of the combined class of $100+n$ students are respectively $50$ and $350$,then the sum of variances of classes $A$ and $B$ is:

If $G_1$ and $G_2$ are the geometric means of two series of sizes $n_1$ and $n_2$ respectively,and $G$ is the geometric mean of their combined series,then what is $\log G$ equal to?

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

If the sum of the deviations of $50$ observations from $30$ is $50$,then the mean of these observations is:

Which one of the following is false?