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: \(7770, 10200, 954, 1640, 23000, 20100\)
- What is the median of Sample A?
- What is the median of Sample B?