Relationship between coefficient of dispersion and percent of data points above the median?

If I know the coefficient of dispersion and the median of a data set, is it possible for me to then calculate the percent of data points that are above the median?

For example, what if the median is 1 but the dataset is all 1's? Would standard deviation help for this?

• Do you know what the definition of the median is? – jbowman May 31 '18 at 20:40
• If the data are constant you can report that fact directly. There is no reason to report any measure of variability, but the SD is 0 (or indeterminate if $n = 1$ and $n - 1$ appears in the divisor). – Nick Cox May 31 '18 at 23:31

The median is always exactly in the middle of all data points. By definition, if there are $N$ data points there will always be $\frac{N-1}{2}-1$ data points above the median for an uneven number of elements in the dataset and $\frac{N}{2}-1$ above the median for an even number.
Therefore, the percentage of numbers above the median is thus given by $\frac{1}{2} -\frac{3}{2N}$ (for uneven number of datapoints) and $\frac{1}{2}-\frac{1}{N}$ (for even number of datapoints).