Maths 101: the mean vs the median [View all]
Last edited Sun May 31, 2015, 07:05 AM - Edit history (1)
Looking at threads like http://www.democraticunderground.com/10026750894 , it's obvious that a good number of DUers don't understand the difference between a mean and a median (and that a lot of those DUers think that they do, and are attacking the OP on the basis of their error).
The mean average of a group of numbers is the sum of the numbers in the group, divided by the number of things in the group. So, for example, the mean of 2,3,5,9,11 is (2+3+5+9+11)/5 = 6.
The median average of a group of numbers is the one in the middle, when they are ordered. So the median of 2,3,5,9,11 is 5, because there are an equal number of numbers smaller than it and larger than it.
The advantage of the mean is that it captures information about all the numbers. If I add 1 to any of the numbers in my set, the mean will go up by 1/n, where n is the number of things I have.
The advantage of the median is that it ignores outliers, which is often a useful thing when looking at sets of data in the real world. In particular, the median income is *not* - whatever some of the people in that thread think - skewed by the income of the very rich (or the very poor) - all it will measure is the income of the middle member of the middle class.
The mean of the set $10k, $10k, $10k, $20k, $10000k is $2010k - the presence of a single multimillionaire massively distorts the mean. But the median is $10k, which gives a much clearer picture of how the average person is living.
(For added credit, the mode average of a set of numbers is the number that occurs the most times - so $10k in the above example. It's generally not very useful. But understanding the difference and the different uses of the mean and median is vital if you don't want to make a fool of yourself).
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