If the median and the range of four numbers $\{x, y, 2x + y, x - y\}$,where $0 < y < x < 2y$,are $10$ and $28$ respectively,then the mean of the numbers is

The mean and the variance of five observations are $4$ and $5.20,$ respectively. If three of the observations are $3, 4,$ and $4,$ then the absolute value of the difference of the other two observations is

The mean of $5$ numbers is $18$. If one number is excluded,their mean becomes $16$. Then the excluded number is

The mean and standard deviation of $20$ observations are found to be $10$ and $2$ respectively. On rechecking,it was found that an observation $8$ was incorrect. Calculate the correct mean and standard deviation if the wrong item is omitted.

The mean of a series $x_1, x_2, \dots, x_n$ is $\bar{X}$. If $x_2$ is replaced by $\lambda$,what will be the new mean?

Suppose that the mean and median of the non-negative numbers $21, 8, 17, a, 51, 103, b, 13, 67$ $(a > b)$ are $40$ and $21$, respectively. If the mean deviation about the median is $26$, then $2a$ is equal to: