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The median is the middle value in a set of numbers. In the set [1,2,3] the median is 2. If the set has an even number of values, 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 is skewed upwards by just a few high values. The average income of a nation might be $20,000 but most people are much poorer. Many people with $10,000 incomes are balanced out by just a single person with a $5,000,000 income. Therefore the median is often quoted because it shows a value that 50% of the country makes more than and 50% of the country makes less than.