Statistics Lesson: Median

Find the "Median" of a set of numbers

What is a Median?

The median is the middle value in an ordered set of numbers. In the set {1,2,3} the median is 2. If the set has an even number of values (so it doesn't have a "middle" value), the median is the average of the two in the middle. For example, the median of {1,2,3,4} is 2.5, because that is the average of 2 and 3.

The median is often used when analyzing statistical studies -- for example, the income of a nation. While the arithmetic mean (average) is a simple calculation that most people understand, it could be skewed upwards by just a few high values. The average income of a particular nation might be $20,000 even though most people are much poorer. Thousands of people with $10,000 incomes are balanced out by just a single person with a $5,000,000 income. This is an example where median income is more useful in representing the living standard of the country. In this case it shows a value that 50% of the country makes more than and 50% of the country makes less than, i.e. what does a person in the middle earn?