## 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