Opinion: Degrees of unfairness

“Median family income declines” (Jan. 11) could be informative about the change in standard deviation in Vermont household income: Standard deviation indicates the degree of disparity among the elements of a population.

http://www.rutlandherald.com/article/20110115/OPINION02/701159999

Published January 15, 2011 in the Rutland Herald

Degrees of unfairness

“Median family income declines” (Jan. 11) could be informative about the change in standard deviation in Vermont household income: Standard deviation indicates the degree of disparity among the elements of a population. For instance, if 10 boys have 50 candy bars apiece, the degree of disparity would be a standard deviation of 1. Now, if a wealthy uncle promised to give the boys an average of 50 candy bars apiece but gave four of them 40, two of them 50 and the last four 60, the average would still be 50 apiece, but the standard deviation would be about 9.428. If, on the other hand, he gave nine of the boys three candy bars each and one boy 473, the average would still be 50 each, but the standard deviation would be 148.627, indicating more than 15 times the disparity. One can imagine how the nine boys would feel about the fairness of the latter situation.

If we look at national household aggregate income for 2007, we can use the candy bar analogy. As in Vermont, the median income has declined slightly over the last 40 years. If we look at just the bottom 94 percent of household income spread, we find a disparity that can be expressed as 3.926, or about half the disparity of a 40-50-60 candy bar split. When we add in the aggregate income for the top 6 percent, we get a standard deviation that can be expressed as 453.657, a disparity 115 times greater than the manifestly unequal 27-473 candy bar split.

The median income treated in the article is just a way of saying that some boys have lost some candy bars. It would help readers more to know where the candy bars went.

CHUCK GREGORY

Springfield