Let the median and the mean deviation about the median of $7$ observations $170, 125, 230, 190, 210, a, b$ be $170$ and $\frac{205}{7}$ respectively. Then the mean deviation about the mean of these $7$ 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?

If both mean and variance of $50$ observations $x_1, x_2, \ldots, x_{50}$ are equal to $16$ and $256$ respectively,then the mean of $(x_1-5)^2, (x_2-5)^2, \ldots, (x_{50}-5)^2$ is

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

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.

Two sets,each of $20$ observations,have the same standard deviation $5$. The first set has a mean $17$ and the second a mean $22$. Determine the standard deviation of the set obtained by combining the given two sets.