To find the median with an even number of values, follow these steps:
- Arrange the numbers in ascending order.
- Identify the two middle values. For an even number of observations nnn, the middle values are the n2\frac{n}{2}2nth and (n2+1)\left(\frac{n}{2}+1\right)(2n+1)th observations.
- Calculate the median by taking the average of these two middle values:
Median=(value at n2)+(value at n2+1)2\text{Median}=\frac{(\text{value at }\frac{n}{2})+(\text{value at }\frac{n}{2}+1)}{2}Median=2(value at 2n)+(value at 2n+1)
For example, for the data set {1,2,2,3,3,4}\{1,2,2,3,3,4\}{1,2,2,3,3,4}:
- Sort the data (already sorted here).
- n=6n=6n=6, so the middle values are the 3rd and 4th observations, which are 2 and 3.
- Median = 2+32=2.5\frac{2+3}{2}=2.522+3=2.5.
This means that when you have an even number of data points, the median is the average of the two central numbers in the sorted list.
