What is the relation between the mean and the median of a discrete data set?

Let $a_1, a_2, \dots, a_{101}$ be a group of real numbers such that $a_i > a_{i+1}$ for all values of $i$ and the mean square deviation of the group is minimum about the number $a_{51}$. Then the mode of the group will be:

For a normal distribution,which of the following relations holds true?

The sum of the absolute deviations is minimum when taken with respect to:

If the mode of a distribution is $18$ and the mean is $24$,then what is the median?

If in a frequency distribution,the mean and median are $21$ and $22$ respectively,then its mode is approximately