The mean and variance of seven observations are $8$ and $16$,respectively. If $5$ of the observations are $2, 4, 10, 12, 14$,then the product of the remaining two observations is

Two data sets each of size $5$ are given. If the variances are $4$ and $5$ and their corresponding means are $2$ and $4$ respectively,then what is the variance of the combined data set?

For a group of $100$ observations,the arithmetic mean and standard deviation are $8$ and $\sqrt{10.5}$ respectively. The mean and standard deviation of $50$ items selected from these $100$ observations are $10$ and $2$ respectively. Then the standard deviation of the remaining $50$ observations is

If the algebraic sum of deviations of $20$ observations from $30$ is $20$,then the mean of the observations is:

While calculating the mean and variance of $10$ readings,a student wrongly used the reading $52$ for the correct reading $25$. He obtained the mean and variance as $45$ and $16$ respectively. Find the correct mean and the variance.

The median of $100$ observations grouped in classes of equal width is $25$. If the median class interval is $20-30$ and the number of observations less than $20$ is $45$,then the frequency of the median class is: