Everybody knows what the word “average” means and that it is the most widely used simple statistic. But it can be highly misleading.
That occurred to me in two recent news reports.
One article a week ago detailed how households would be affected if we returned to the tax rates in effect from 1994 to 2001, including an elaborate tabulation of the average annual increase for taxpayers by state.
The second article dealt with average life expectancies relating to the solvency of Social Security and Medicare.
In the first article, the tax increases detailed ranged from an average of about $1,600 per taxpayer for low-income states to more than $4,000 for a couple of high-income ones.
An online commentary by Yahoo analyst David Chalian emphasized that if the Bush tax cuts are allowed to expire for all, the average tax collected nationwide would go up by more than $2,000 per taxpayer.
Both are correct. But both ignore the fact that using an average in this case can be highly misleading because increases for individual taxpayers are widely dispersed, and the distribution is highly skewed, as are income taxes paid in any year.
A lot of taxpayers owe relatively small amounts of tax, from a few hundred to a few thousand dollars. A very small number face large tax bills running from tens of thousands to many millions of dollars.
As champions of the Bush tax cuts like to say, these cuts reduced amounts due for everyone because marginal rates at all income levels were reduced. This is correct. But critics of the cuts are also correct in pointing out that the bulk of the tax reduction went to the relatively small number of high-income taxpayers. That is because the highest 20 percent of households pay the large majority of all income taxes collected.
A news report saying that the “average tax increase will be $2,000” will lead many people to assume that they, themselves, will face such an increase when, in fact, well over half of taxpayers will see tax increases of less than $500.
Most people don’t save tax materials in enough detail to go back and see how much their tax bills were reduced by the 2001 and 2003 tax changes. But for my wife and me, comfortably in the upper-half of the income distribution, the reduction was well under $1,000 a year.
A second case of misinterpreted averages is that of “life expectancies,” the average age to which someone born in a particular year would live if the mortality rates at each age stayed the same over that person’s whole life.
These expectancies are often used in connection with Social Security and Medicare. People argue that these programs are doomed because of rising life expectancies.
For example, since the first Social Security checks went out in 1940, life expectancy has increased from 62.9 years to over 79 in 2012. In 1965, when Medicare was passed, it was about 69. So, the argument goes, the financial problems of these programs stem primarily from the fact that people are living longer.
That is certainly a factor. But the expectancies cited are “expectancies at birth” that take into account deaths at all ages. Most of the increases cited are due to reductions in deaths among infants and children, not because most people live dramatically longer.
Considering people only at age 65, average life expectancy has increased by less than six years since 1940 and less than three years since 1965. So calculations made back then about program benefits were neither cynical nor inept.
Yes, for both programs, we are going through marked increases in the number of beneficiaries per younger person paying FICA taxes to support the programs. This is a genuine problem, foreseen by many, even if not by members of Congress who have dragged their heels for nearly two decades in fixing it.
But actuaries and demographers have known for decades that 81 million people were born from 1946 through 1964. These made the number of taxpayers higher from the 1960s until about now and will make the number of beneficiaries higher as they now retire.
In both cases, tax increases and life expectancies, one can get a better idea of the situation if one knows the median as well and the average or mean. If you take all the different amounts, say in taxes paid, and put them in order from highest to lowest, the median is the number right in the middle. Half pay less than this amount and half pay more.
If you take all income-taxpaying households, the average increase they would see with the expiration of the Bush tax cuts would be about $2,000. But if you rank them from greatest increase in tax due to lowest, the median is less than $400. Half of all taxpayers will see an increase of that amount or less.
Unfortunately, simple averages are tabulated and used much more frequently than medians, simply because less data is needed. All you need to know is total taxes paid and total number of taxpayers. For a median, you need to have information on each individual taxpayer, or at least on the number that fall into different dollar categories.
Income distribution is one issue for which medians are commonly presented. For example, in the two decades from 1990 to 2010, average U.S. household incomes, adjusted for inflation, increased from $60,487 to $67,530, or 11.6 percent. But the median income only went from $48,423 to $49,445 or about 2.1 percent. Income in the poorest 40 percent of the population has been falling rather than rising. Knowing the median gives a much different picture than the average, just as it does with tax changes related to the Bush tax cuts.
St. Paul economist and writer Edward Lotterman can be reached at email@example.com.