1.2 Median

The median is simply the 'middle' value, meaning that 50% of the values are higher, and 50% lower, than the median. Going back to our previous example where we had \(n=5\) income values: \(1740, 6940, 25000, 1170, 66300\), we can calculate the median in two steps.

First, we list the values in order from lowest to highest: \[1170, 1740, 6940, 25000, 66300\]

Then, we take the middle value, which in this case is \(6940\). It was straightforward to take the middle value in the above example, because we had an odd number of values, \(n=5\).

What happens if we have an even number of values, for example, \(n=6\)? Well, suppose we now want to know the median of the following \(n=6\) income values: \(1740, 6940, 25000, 1170, 66300, 12100\). Our first step is still the same - we list the values in order from lowest to highest: \[1170, 1740, 6940, 12100, 25000, 66300\]

This time, the two middle values are \(6940\) and \(12100\). So, to find the median, we need to find the mean of those two values, which can be done as follows: \[(6940 + 12100) \div 2 = 9520.\]

Your turn: Consider the following two sets of sample values:

  • Sample A: \(7770, 10200, 954, 1640, 23000\)
  • Sample B: \(7770, 10200, 954, 1640, 23000, 20100\)
  1. What is the median of Sample A?
  2. What is the median of Sample B?
  1. 7770
  2. 8985

These notes have been prepared by Amanda J. Shaker. The copyright for the material in these notes resides with the author named above, with the Department of Mathematics and Statistics and with La Trobe University. Copyright in this work is vested in La Trobe University including all La Trobe University branding and naming. Unless otherwise stated, material within this work is licensed under a Creative Commons Attribution-Non Commercial-Non Derivatives License CC BY-NC-ND