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

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

Consider the following statements:
$(1)$ Mode can be computed from a histogram.
$(2)$ Median is not independent of change of scale.
$(3)$ Variance is independent of change of origin and scale.
Which of these is/are correct?

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:

Let $x_1, x_2, \ldots, x_{11}$ be the observations satisfying $\sum_{i=1}^{11}(x_i-4)=22$ and $\sum_{i=1}^{11}(x_i-4)^2=154$. If the mean and variance of the observations are $\alpha$ and $\beta$,then the quadratic equation having the roots $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$ is

If the mean and variance of eight numbers $3, 7, 9, 12, 13, 20, x$,and $y$ are $10$ and $25$ respectively,then $x \cdot y$ is equal to