# Mathematical Mistake: Averaging Multiple Statistical Sources Together to Form One “Overall” Average Income Figure

This article first appeared in the spring 2008 issue of the Expert Witness.

In estimating a plaintiff’s without- or with-incident income, there is a mathematical mistake that an economist can make that will potentially have a large impact on the resulting income path and, subsequently, on the plaintiff’s loss of income. This mistake is the practice of averaging multiple statistical sources together to obtain one “overall average”. It may seem reasonable, at first glance, to assume that averaging multiple sources of statistical data would result in an overall average which is superior to the quality of the individual averages. However, this is often not the case. This approach can lead to an incorrect and misleading estimate of a plaintiff’s income due to double-counting, a failure to take into account differing quality of each source (as measured by sample size), and the inclusion of important characteristics (such as age, education, and gender) that are not applicable to the plaintiff. This method also has the potential to provide misleading estimates simply based on the choice of the sources used in calculating this “average”.

To illustrate these effects, we have summarized in the table below, the average income for partsmen (as an example) obtained from a number of common statistical data sources.

As shown in the table, if we were to “average” across all of the incomes then we would get an income figure of \$44,567 (in 2008 dollars). However, this would be an incorrect and potentially misleading estimate of the average income of partsmen.