Measures of central tendency in political decision-making and wealth assessment

¶ … median and the mode. The mean is the average of the total set, the median is the middle of the total set and the mode is the most frequently reported number of the total set. The median can be found by literally writing the numbers in a string, and then finding the number that sits exactly in the middle. When measuring family wealth in order to make political decisions, it is the median that is the most important of these three (Boeree, 2005).

The mean reflects the average of all the different numbers within the set. The mean is not a bad number with which to work, but it can be skewed upward or downward by very large outliers. For example, consider the set 1, 1, 3, 4, 2, 3, 1, 22. The mean of this set is 4.625. The median is 2.5 and the mode is 1. The mean is above all of the numbers in the set, except for one number (22). If these were measures of family wealth, the one rich family (22) would skew the national figures to make the country look much richer than it actually is. 7/8 of the country would actually fall below the mean. Large outliers skew the mean, and this happens with family income as well. Some American families have wealth that is in the billions, or even just the hundreds of millions. That wealth is equivalent to hundreds or even thousands of ordinary families. As a result, the mean figure is skewed upward, and probably lies in the 70th or 80th percentiles, rather than the 50th percentile where it should be.

The mode is equally troublesome in this instance. The mode in the example set is 1, because it is the most frequently reported number. However, the mode is at the low end of the figures reported. It happens that the mode is reported more than any other, but it does not represent the typical experience. When looking at American family wealth, it is entirely possible that the mode will lie at a very low number as well, since the number of destitute family units may well be high -- they are bounded at zero, while there is no upward bound so the figures will be stretched out. By contrast, the poorest families will be clustered at very low numbers, and therefore the mode is likely to be one of these very low numbers, if not zero.

The median is the best measure to use. By definition, it sits in the middle of the set. This encompasses the most accurate number because it reflects more closely the larger amount of numbers within the set. The median cannot be skewed like the mean can be, by large outlying numbers. Whether the numbers at the top and bottom of the set are significant outliers or not is irrelevant to the median. The mode is also skewed by not only the fact that random chance plays into what number will be the mode but also by the fact that there is likely to be a clustering of responses at the low end where the zero bound creates a constraint.