The median is the middle value in a set of numbers sorted in ascending or descending order
. It separates the higher half from the lower half of a data sample, population, or probability distribution
. It is also known as the 2nd quartile, 5th decile, and 50th percentile
. To calculate the median
:
- Arrange the data in ascending order.
- If there is an odd number of data points, the median is the middle number. The formula to find the median is $$ \left(\frac{n+1}{2}\right)^{th} $$ term, where n is the number of observations
. For example, the median of 2, 5, and 8 is 5
- If there is an even number of data points, the median is the average of the two middle numbers
. The formula to find the median is $$ \frac{\left(\frac{n}{2}\right)^{th} \text{ term } + \left(\frac{n}{2} + 1\right)^{th} \text{ term}}{2} $$, where n is the number of observations
. For example, the median of 4, 5, 6, and 7 is 5.5 (the mean of 5 and 6)
The median is often compared to the mean (average) and mode in statistics
. The median is less affected by outliers than the mean, making it a better representation of the center of a data set with extreme values
