# The Mean and the Median Tell Two Different Stories

Averages, if you’re not careful, can as easily mislead as enlighten.  It matters a lot which statistical measure of the “average-ness” that’s used.  A good example comes in the case of the U.S. long-term trend of economic growth.  What we’re interested in is to what degree the amount of GDP the average household has available has increased over time.  It’s the prime way economists measure whether not living standards are improving.  GDP, of course, is the measure we use to count output in the economy.  GDP is the total market value of all goods and services produced for final demand in a year.   Real GDP is the inflation-adjusted version of it so we can compare GDP from different years.   But of course, just because total GDP, or even real GDP, is going up from year to year is no assurance that living standards are generally increasing.  After all, if real GDP grows by 1% per year but the population grows by 2% per year, there’s less per mouth each year.

So we need to adjust the real GDP measure to account for population growth. We want a measure of average GDP per person or average GDP per household.  Those readers who didn’t fall asleep in statistics class might recall that technically “average” isn’t a statistical measure.  Instead there are several different ways of calculating what statisticians prefer to call “central tendency” instead of “average”.  The two most common calculations in economics are the mean and median.  And there’s a huge difference between them.  The mean is  what you probably learned in primary school as the “average”.  To calculate it we take the total and divide by the number of people in the population.  When economists cite GDP per capita, we are, in fact, calculating the mean Real GDP per person.  The mean, the real GDP per capita for the U.S. over the last 34 years has grown at around a 1.9% annual rate.  That might not sound like much, but remember the power of compounding means that at 1.9%, mean real GDP per person will double in less than 40 years – one working lifetime.  Sounds good, right?  Sounds like the American dream in action, right? Wrong.

Real GDP per capita when looking at the U.S. is highly misleading because most of the growth only goes to the top 1% income folks.  The vast majority of Americans, the other 99% of us, haven’t experienced anything like that growth.  To see the difference let’s consider real income of the median household.  Remember Gross Domestic Income is the same as Gross Domestic Product.  It’s just counted differently by counting income available to spend instead of actual spending.  Long run, they are the same.  Now let’s quick review what the median is. The median is the middle observation. It means that there’s as many observations with a lesser value as there are with a greater value.  In this context it means that there are exactly as many households with a smaller income as there are households with a larger income.  It’s another way of looking at the average.  In this case we’re looking for the most typical household.  Statistics note:  mean will equal median if both sides of the distribution are identical, but in income this isn’t true – millionaires, billionaires, and rich households are a lot richer than the \$49,700 median income but the poorest households can only \$49,700 poorer at most.

In the U.S. over the last 34 years, the median household income has only grown at less than 0.5% per year despite increases in education.  So real GDP per person grows at 1.9% per year, but real median income only grows less than 0.5% per year.  At 0.5%, it will take 150 years for income to double.  End of the American dream of doing a lot better than your parents. What accounts for the difference?  It’s the upper 1% of the income distribution, the rich folks, millionaires and billionaires, that have skimmed off the 65% of all of the GDP gains for 34 years.

Princeton economics professor Uwe Reinhardt explains in the NYTimes Economix blog:

So if an American macroeconomist — a specialist who tends to think of nations as people — or high-level government officials or politicians mimicking a macroeconomist boasted on a television talk show that “average family income grew by 3 percent during 2002-7, more than in most European economies,” about 99 percent of American viewers, reflecting on their own experience, would probably scratch their heads and wonder, “What is this guy talking about?”

The third chart, below, exhibits the growth path of real G.D.P. per capita in the United States over the period 1975-2009 and the corresponding path of real median household income. The data show that over the 34-year period, real G.D.P. per capita rose by an annual compound rate of 1.9 percent. Those data come from the Economic Report of the President to the Congress (Tables B-2 and B-34).

Sources: Economic Report of the President to Congress (G.D.P.); Census Bureau (income)

According to the Census Bureau data (see Table H-6), however, median household income in the United States rose by less than 0.5 percent a year. Other than national pride in league tables, that 1.9 percent average economic growth does not mean much for the experience of the median household in the United States.

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