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Wealth: Median and Mean

If you're well familiar with the difference between these two terms, skip this section and continue on. There is useful data following this explanation.

News headlines frequently provide rosy news about total income, or total wealth, or productivity gains. Sometimes they will report that such-and-such a measure is up X% in total, or that the average per capita something-or-other is up Y%, or that the median of yet a third measure is up Z%. These are usually treated as unmitigated causes for widespread relief and satisfaction.

The truth, however, is often a bit more complex, and knowing what you're reading -- and noticing what is not being said -- is not all that difficult. Here's a primer to get you started.

Total — When the total of a particular measure rises, that sounds as if it should be good for everyone, right? One might infer that this is good for all of us; that we are all likely to be sharing in it equally, or at least that some of the benefit will "trickle down" to most of us. Maybe. But keep in mind that population continues to increase, and that the increase in whatever measure may not be enough to keep up with population growth, or may look a lot less impressive when population growth is factored in. (Population growth is usually sufficiently small year to year that we don't need to think about it, except when one starts looking at places like, say, Las Vegas, whose population has been rising rapidly.)

Average, "mean," "per capita" or "per household" — This measure factors out population growth, so it tells you a bit more than you knew before. But it still doesn't tell you anything about how the gains are distributed. Do we all get equal amounts? Do 70% of us get some and 30% of us none? Do 50% of us gain nothing, 50% get something, and 90% of the gain go to 5% of us?

"Average" and "typical" are two different things, and even if you are from Lake Wobegon, where all the children are above average, the odds are strongly against any particular person making out as well as "average," if the measure being discussed has to do with income or wealth. Depending on the measure, about 75% of us are "below average," and sometimes the percentage is a lot higher than that! (see "median as a percent of mean")

How could 75% of us be "below average," you ask? And surely if that's true, you are probably part of the 25% who are "above average," aren't you? Or you will be, soon, when, as the old expression goes, your "ship comes in."

Before I answer that first question, let me go to the third measure you need to know about, the Median. Median is a measure of the "typical" individual or household. More precisely, if one is looking at a population of 100 people, and lines them up by income, or wealth, or height, the income, wealth or height of #50 is the median: half have less, half have more. This gives you a sense of the middle that is not affected by what happens to the people who have very low or very high amounts of whatever is being measured. Adding three basketball players to the group doesn't change the median height much, though it may increase the mean a bit; replacing any three people in the 100 with three basketball players won't change it much either. Adding Paul Bunyan to the group may also increase the mean, but doesn't affect the median height much. Similarly, adding Bill Gates to a group of people with more ordinary wealth or income may increase the mean a great deal, but doesn't change the median.

Okay. Those who have skipped the explanation are back with us. Let's proceed.

Two of the striking things one notices when one looks at the wealth distribution data are

(1) how concentrated wealth is, and
(2) that, despite the ownership of homes, stock and retirement assets becoming more widespread, overall wealth is becoming more concentrated.

How does this relate to totals, means and medians? Well, if we hear that, say, productivity has increased by x% over the same period year ago, is that good news for everyone listening, or is it only good news for some of us? To whom should productivity gains go? Should workers benefit from it? Should those who invest in manufacturing plants and equipment be the beneficiaries? Should those who invest in land be the beneficiaries? Should top management be the main beneficiaries? If those benefits are going disproportionately to one of those groups, is it just to collect some of that benefit by taxation of particular kinds of income?

Median as a Percent of Mean

When both the median and the mean are provided, you can get a sense of the distribution of the data. Many of the studies on this website provide both medians and means for income or wealth, or subsets of it, and some also provide trend data. Wealthandwant has added rows or columns to the appropriate tables so that you don't need to calculate the median as a percent of mean. The trend you'll see is that the median as a percent of the mean is generally dropping across time. When you delve into the data, you'll see that what is going on is a major increase in the wealth or income among those in the top 1%, and sometimes the next 4% and occasionally 5%. Seldom do you see even the second 10%'s share increasing.

Here are some tables on this website which show "median as a percent of mean"

1. Currents and Undercurrents: Changes in the Distribution of Wealth, 1989–2004

Table 3: Mean, 10th and 25th percentiles, median, 75th and 90th percentiles of the distribution of net worth; 1989–2004.

2. Recent Changes in U.S. Family Finances: Evidence from the 2001 and 2004 Survey of Consumer Finances

Table 1. Before-tax family income, percentage of families that saved, and distribution of families, by selected characteristics of families, 1995–2004 surveys

Table 3. Family net worth, by selected characteristics of families, 1995–2004 surveys— Thousands of 2004 dollars

3. The Unraveling of the American Pension System, 1983-2001

Table 1: Mean and Median Wealth and Income, 1983-2001 (In thousands, 2001 dollars)

Table 5. Mean and Median Pension Wealth for Households in Age Group 47-64, 1983-2001 (In thousands, 2001 dollars)

Table 7. Mean and Median Net Worth and Private Accumulations, For Households Aged 47-64, 1983-2001 (In thousands, 2001 dollars)

4. ASSET POVERTY IN THE UNITED STATES: Its Persistence in an Expansionary Economy

Table 1B Wealth Measures by Percentile, 1984–99

 

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