The median of a set of $19$ observations is $30$. If two observations with values $8$ and $32$ are added,what is the median of the new set of $21$ observations?

Find the weighted mean of the first $n$ natural numbers,where the weights are equal to their squares.

If a variable takes the discrete values $\alpha - 4, \alpha - \frac{7}{2}, \alpha - \frac{5}{2}, \alpha - 3, \alpha - 2, \alpha + \frac{1}{2}, \alpha - \frac{1}{2}, \alpha + 5$ (where $\alpha > 0$),then the median is:

The mean of a set of observations is $\bar{x}$. If each observation is divided by $\alpha$ $(\alpha \neq 0)$ and then increased by $10$,what is the mean of the new set?

The median of a set of $9$ distinct observations is $20.5$. If the four largest observations of the set are increased by $2$,what will be the median of the new set?

The mean and the median of the following ten numbers in increasing order $10, 22, 26, 29, 34, x, 42, 67, 70, y$ are $42$ and $35$ respectively. Then,$\frac{y}{x}$ is equal to: