To find the median with an even number of values, you always end up taking the average of the two middle numbers.

Quick Scoop

When your data set has an even count of numbers:

  1. Arrange all the numbers in order (smallest to largest).
  2. Find the two middle positions: n/2n/2n/2 and (n/2)+1(n/2)+1(n/2)+1, where nnn is how many numbers you have.
  1. Look up the values at those two positions.
  2. Add those two values and divide by 2.
    In formula form (for a sorted list):
    Median=value at (n/2)+value at ((n/2)+1)2\text{Median}=\dfrac{\text{value at }(n/2)+\text{value at }((n/2)+1)}{2}Median=2value at (n/2)+value at ((n/2)+1)​.

Simple example

Say your numbers are:

  • 1, 3, 5, 7, 9, 11 (so n=6n=6n=6, an even number).

Steps:

  1. They’re already in order.
  2. Middle positions are 6/2=36/2=36/2=3 and 6/2+1=46/2+1=46/2+1=4.
  1. The 3rd number is 5, the 4th number is 7.
  1. Median =(5+7)/2=6=(5+7)/2=6=(5+7)/2=6.

So even though 6 is not actually in the list, it’s still the median because it sits exactly between the two middle values.

Why it works (quick intuition)

  • The median is the middle position of the data, not necessarily one of the original numbers.
  • With an even count, there’s no single middle number, so the “middle” lies halfway between the two central values.

If you’d like, tell me a specific list of numbers and I’ll walk through the median step-by-step with you.