In a previous post I investigated the question of whether those in Howard County with annual incomes of \$120,000 or more truly constituted the “wealthy few” or not. (The answer: No.) Key to that investigation was the idea of median household income, as reported by the US Census Bureau in its annual Amercian Community Survey. It turns out that the ACS data provide some interesting insights into what makes Howard County special, and can help explain the nature of the conflicts that have raged over the future of Howard County in general and Columbia in particular.

In this post I’ll start with a concept that is easy to understand but has interesting implications, namely median income and its relationship to average (or mean) income. Let’s suppose we want to look at household incomes in Howard County or any other jurisdiction. We can compute the mean income (to use the preferred term) by adding all the household incomes and then dividing by the number of households. To simplify things, let’s assume we have only 10 households with incomes as follows:

\$16,000 \$37,000 \$56,000 \$75,000 \$92,000 \$111,000 \$132,000 \$163,000 \$190,000 \$317,000

The sum of all incomes is \$1,189,000, and then we divide by 10 to get an mean (or average) income of \$118,900. Simple enough, right?

Wrong. The problem with mean income is that it doesn’t necessarily represent the reality for the “typical” household, because it can be skewed by households that have either disproportionately small or (especially) disproportionally large income. For example, let’s suppose that the highest-income household in our example greatly increases its income (perhaps they’ve been the beneficiary of a successful IPO, for example), so that the incomes now look as follows:

\$16,000 \$37,000 \$56,000 \$75,000 \$92,000 \$111,000 \$132,000 \$163,000 \$190,000 \$1,558,000

The total of all 10 household incomes is now \$2,430,000, which divided by 10 gives a mean household income of \$243,000. Thus the mean household income has more than doubled, but the “typical” household (9 out of 10 of them, in this example) sees no improvement in its own income.

To correct for this distortion the Census Bureau and others use a different measure of household income, namely median income. The median income is the income that “falls in the middle”: half of all incomes are lower, and half are higher. In the example we have five households with income of \$92,000 or less, and five households with income of \$111,000 or greater. We then compute the median income as the value halfway between these two incomes, or \$101,500. (This happens to be very close to the Howard County median household income of \$101,672 in 2007; as will become apparent later, I deliberately chose these example numbers to create a microcosm of Howard County.)

Note that in computing the median income we didn’t specify whether we were using the first set of incomes or the second set of incomes (in which the highest-income household greatly increased its income). That’s because it doesn’t matter: the median income is exactly the same in both cases. Using median income thus avoids the distortion inherent in average income, where (as the economics joke goes), Bill Gates can walk into a bar and cause the average income to skyrocket.

But using median income has its own problems as well. Suppose that instead of walking into a bar, Bill Gates moved to Howard County. Or to achieve the same overall effect, 50 billionaires moved into Howard County, or 500 people worth \$100M each. There are almost 100,000 households in Howard County, so adding a few hundred super-rich families isn’t going to affect the county’s median income at all (just as making one family wealthier didn’t affect median income in our toy example). But can anyone doubt that such an influx would change the character of Howard County in major ways?

How could this effect be quantified? That will be the subject of a future post.

#### Steve Lee - 2008-10-01 07:52#

> Bill Gates moved to Howard County. Or to achieve the same overall effect, 50 billionaires moved into Howard County, or 500 people worth \$100M each. Now that *really* puts BG’s worth onto perspective. Definitely not the mode.

#### JessieX - 2008-10-17 03:22#

Welcome, Frank, to the “community listing” inside HocoBlogs. Happy to have your thoughts and perspectives articulated and available to Da Public.

#### Eugene (ewwmko@yahoo.com) - 2008-10-20 15:10#

Nice article. Thanks. :) Eugene