# What percent of values of a data set are less than the median?

Jul 23, 2015

Anywhere between 0% and just under 50%

If all the values in a data set of size $2 N + 1$ are distinct, then

N/(2N+1)*100%

#### Explanation:

If the elements of the data set are arranged in ascending order, then the median is the value of the middle element.

For a large data set with distinct values, the percentage of values less than the median will be just under 50%.

Consider the data set $\left[0 , 0 , 0 , 1 , 1\right]$. The median is $0$ and 0% of values are less than the median.