The median income for households is the point at which one-half of the households have a higher income, and one half a lower income. To be an exact measure, we would need to know the exact incomes of each household in an area. While we do not know this, we utilize the cumulative counts of households in each income range (e.g. $20,000 – $24,999) and estimate the 50% point from this distribution. Again, it must be remembered that this is an estimate, but the bounds of the error of this estimate are at least limited to the income class in which we reach 50% of the households.
The general rule is that for any area, you should minimize the error of the median estimate by using the income distribution for the area itself rather than averaging the median income estimates for its component areas.
To put some concrete bounds on this, we computed the median income for counties by using the county income distribution (the preferred method) and by computing the household weighted average of the median income for its component block groups. The average error was 3.4% which is substantial, but the results for specific counties are surprisingly high –
|County||Households||Median Income||Average of Medians||% Error|
|06037 Los Angeles, CA||3,490,380||$70,948||$76,525||7.9%|
|34013 Essex, NJ||304,897||$64,518||$78,354||21.5%|
|36119 Westchester, NY||362,938||$92,822||$108,651||17.1%|
|48113 Dallas, TX||1,006,294||$61,181||$70,541||15.3%|
23% of the counties had an error of five percent or greater, and 4% had an error rate of over ten percent. So, surprisingly high was perhaps an understatement. This is clear evidence that you should never take the shortcut of averaging medians! Please do check the documentation for your particular software platform and make sure that your “median income” figures are just that and not averaged medians.