The total expenditure incurred by an industry under different heads is best presented as a

The mean and standard deviation of the marks of $10$ students were found to be $50$ and $12$ respectively. Later,it was observed that two marks $20$ and $25$ were wrongly read as $45$ and $50$ respectively. Then the correct variance 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?

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:

The mean and standard deviation of $100$ observations were calculated as $40$ and $5.1$,respectively,by a student who took by mistake $50$ instead of $40$ for one observation. What are the correct mean and standard deviation?

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