# U.S. income inequality, median vs mean income

Last week the U.S. Bureau of the Census came out with its annual report of United States household income and poverty in the United States. The news was good. Median household income increased in 2016 for the second year in a row. In 2016 median household income reached $59,039 — a 3.2 percent increase after inflation over the 2015 number.

That good news got me to wanting to look at the data more closely, so I downloaded the Census Bureau data in a spreadsheet. Not only did I get data on the median household income, but I got the mean as well. that got me to thinking, "What if I could compare the median to the mean?" The first thing I noticed was that for the recent years of data, the mean or average household income was much higher than the median.

Now the median is the income level that is right in the middle. Half of all households have an income level that is higher than the median, and half have an income that is lower. And since the average income is much higher than the median, it has to be that there is much a lot of income at the extreme top half of the income distribution.

Higher income extremes in the top half of the distribution of income is pulling up the average.. A perfectly equal distribution would result in the average income and median income being equal. The difference between the mean or average household income from the median tells us something about income inequality in the United States.

To get a picture of how income inequality has changed over time, I made a graph of of the median and mean income. I used the online tools provided by the St. Louis Federal Reserve (FRED).

Here is a picture of that graph.

The blue line is the mean or average household income, the red line is the median and the green is the difference between them. It is clear that the difference between the mean and median has grown steadily.

Now I was curious. Economists are always concerned with the distribution of income, so I figured that there must be some discussion of the mean and the median household income and what it signifies for inequality. So I did a google search, and found a blog post in FredBlog, "The mean vs. the median of family income," posted by Christian Zimmermann.

Zimmermann pointed out that while the difference between the mean and median income was indeed increasing, it would mean increased inequality only if the absolute difference between the two measures were growing. To be a conclusive sign that inequality is increasing - we know it is, since there are many other measures economists use that show inequality increasing - , the percentage difference or the ratio between the mean and the median income need to be increasing. .

Zimmerman has a point, so I recreated his graph of the ratio of mean to median income.

You see how dramatically the ratio of mean or average income to median income has increased over time. Yes, this measure documents the increase in income inequality in the United States, just as so many other measures do.

To paraphrase a familiar saying, "The rich get richer relative to those not rich."