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The mean vs. the median of family income


FRED has several datasets to help you investigate the distribution of income. One of them is the Income and Poverty in the United States release from the U.S. Census Bureau.

The graph above shows real family income in the United States in constant (2013) dollars. The mean is the average across all families. The median identifies the family income in the middle of the sample for every year: half of incomes are higher, half are lower. We quickly learn three things from this graph: 1. Family income has been growing much more slowly since the 1970s. 2. There are several episodes of declining income, and they become increasingly long and deep. 3. Median and mean incomes are diverging.

The last point could be an optical illusion, though, because both series have increased over time and their relative difference may have stayed constant even though the difference has increased in absolute terms. To make sure, we divide the mean by the median in the graph below; we can see that, indeed, this ratio has increased. But what does that mean? If the distribution of income is uniform (if every family has the same income), the ratio will be 1. If the distribution is unequal, the ratio will be higher than 1. For example, imagine we start with a uniform distribution of income and then the top 10% of families double their income. The median would not change, but the mean would increase by 10%. The data in the graph below clearly show that there has been an increase in inequality in family income, with a dramatic jump from 1992 to 1993.

How these graphs were created: Under “Sources,” find the Bureau of the Census and choose the Income and Poverty in the United States release. The mean and median real family income series should be among the top choices. Select them and add them to the graph. For the second graph, add the mean series as before; but, instead of adding the median series as a separate series, add it to the mean series (series 1). Finally, expand the “Create your own data transformation” panel and apply formula a/b.

Suggested by Christian Zimmermann

View on FRED, series used in this post: MAFAINUSA672N, MEFAINUSA672N


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