A Tale Of Two Statistics

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These two figures nicely express the growing economic inequality in our society:

Average U.S. household’s net worth = $522,000
Median U.S. household’s net worth = $61,000

Averages are calculated by adding up a list of numbers and then dividing the sum by the number of numbers in the list. For instance, the average of this list of five numbers is 20: {1, 2, 3, 4, 90}, because their sum is 100, and 100/5=20. Medians, on the other hand, are by definition the middle numbers of such ordered lists; the median of our list is 3.

Now, if the list is linear and symmetrical, the average and the median will be the same, as it is in this list: {1, 2, 3, 4, 5}. Notice that the difference between the average here (3 – the same as the median) and the average in the previous list (20 – much higher than the median of 3) is due entirely to the highly irregular value of 90 at the end of the first list, versus the 5 at the end of second list.

An analogous explanation is available for the difference between Average and Median U.S. household’s net worth. The extreme, sharp increase of wealth near the top of the ordered list skews the average of the list much higher than its median.

These figures are given some interesting context in an AP story by Paul Wiseman, entitled “Rising wealth doesn’t generate spending“, which tries to explain why rising wealth of the U.S. as a whole (e.g., the rising average wealth) doesn’t result in more consumer spending-

The biggest gains in wealth are going to wealthy households that tend to save a big chunk of their incomes and spend a smaller proportion on basics such as food and clothing. “Those guys don’t spend much,” says economist Edward Wolff of New York University. The disparity shows up in numbers Wolff calculated. He found that the average U.S. household’s net worth rose this year to $522,000. But the average is skewed higher by the vast net worth of America’s wealthiest — Bill Gates’ $67 billion, for instance, according to Forbes magazine.

So Wolff looked at the net worth of the median U.S. household — those smack in the middle, where half of households earn more and half less. The median family’s net worth is far more modest than the average: $61,000, Wolff estimates. That is $50,800, or 47 percent, short of where it was in 2007.

One reason: The biggest gains have come from the rise in financial markets. And the benefits of the stock market’s surge have gone disproportionately to America’s wealthiest households. Wolff calculates that the wealthiest 10 percent of U.S. households own more than 80 percent of stocks, even including retirement accounts such as 401 (k) plans. “The recent stock market boom has really benefited just the top,” Wolff says.

Moral of the story: always discount reports of averages, or even reports of totals (e.g., GDP), when estimating how informative the given datum is. From such figures, very little can be inferred about how the economy is actually doing for most people. Reports of medians can also be misleading, of course, but they are generally more informative.

3 thoughts on “A Tale Of Two Statistics

  1. I read something about this yesterday. I found it oddly comforting that I was not alone in being broke.

  2. Hi Jim. Yeah, “the 99%” are largely in the same boat, although some of us are closer to steerage…

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