The median is a statistical measure of central tendency, that is, a measure of where the middle of a set of number is. More specifically, the median is the number that splits the numbers into two sets, one higher and one lower, as evenly as possible. For instance, if the numbers are 90, 120, 150, 180 and 260, then 150 is the median. Other measures of central tendency include the mean, or average, and the mode, which is the most common value.
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The Median Is Resistant to Outliers
Outliers are numbers that are unusual. For example, if you are studying the heights of adult male humans, and, by chance, you include a man who is 4 feet 10 inches tall, that person's height would be an outlier. The median is not affected by outliers. This is an advantage because you might not want that person who is especially tall or short to have as much influence as others. But omitting the outlier, as the median does, is also a disadvantage, because you might want the outlier to have some influence.
The Median Deals Well with Skewed Data
A distribution of data is skewed when it has a long "tail," meaning it has many values that are at one end or the other of the distribution and few at the opposite end. It can be right-skew or left-skew. Right skewed data has some values that are much higher than the average, but few or none that are much lower than the average. One common example is income; some people have incomes that are much higher than the average, but the minimum income is 0. The median deals well with skewed data, and this is why you see "median income" reported a lot more than mean, or average, income.
The Median Is Easy to Understand
One advantage of the median is that it is easy to understand and explain, even to "math-phobic" audiences. Although there are formalities to the definition, such as how to deal with tied values, the basic idea of the median is easy to illustrate with an example or two.
The Median Gives No Indication of the Shape of a Distribution
The median only measures central tendency, which can be a disadvantage, as there are more characteristics of a set of numbers. For example, suppose you have two sets of incomes that you wish to compare. One is
$40,000 £29,250 £32,500 £35,750 and £39,000;
the other is
$10,000 £13,000 £32,500 £52,000 and £78,000.
These two sets have the same median -- £32,500 -- but the second set is much more spread out than the first, and the median gives no indication of this.