I'm updating this post by request from some regular readers of the blog. Enjoy. -Dr. Petrosino At a Board of Education meeting in Hoboken, N.J. an interesting exchange occurred between two board members (see video at bottom of this page). One member was essentially requesting a goal of reducing legal fees by 10% (for the past few years, the Hoboken Board of Education has exceeded State of New Jersey guidelines for legal expenses).
Evidently, the use of an average is unacceptable to Hoboken Board of Education member Leon Gold. Initially, Mr. Gold uses an example of the average temperature of Alaska to apparently make his point and then follows it with an assumption that averages are extremely deceptive:
"I mean I suspect the average temperature of Alaska is 50 degrees. Averages are an extremely deceptive number" -Hoboken BOE member Leon Gold
Let's take a look a little more closely. First, the average temperature of Alaska is no where near 50 degrees. According to the NOAA National Climatic Data Center, the average temperature of Alaska is 26.6 degrees. But he says it with such authority and confidence, one would be inclined to trust him. In fact, Alaska is an extremely cold place. The coldest state in the United States by far (North Dakota is a distant 2nd at 40.4 degrees). Perhaps Board member Gold was confused by the average temperature of the United States? (average temperature roughly 52.7) Perhaps he was thinking that such a large land mass would closely parallel the average temperature of the earth? (average temperature generally accepted to be 59 degrees). Its difficult to be sure. But what is clear is that the average temperature of Alaska is no where near 50 degrees. Perhaps having spent time in Alaska and being a STEM educator this misuse of climate data and average made me sensitive and attuned to this mistaken notion. In fairness to Mr. Gold, he did say "suspect" concerning the average temperature of Alaska but when viewed in context (see video below) one can tell that it was said with a fair amount of confidence and arguably...perhaps bravado.
The next assertion Board member Gold makes is that average is an "extremely deceptive" number. I do not want to pretend to know what Mr. Gold means by deceptive but most grade school students understand that an average can be overly influenced by an outlier or multiple outliers. In fact, all one needs to do is to take a look at a list or distribution of the numbers and see if, in fact, there are any outliers. Also, we have measures like standard deviation to determine if we need to pay special attention to representative nature of the average.
I did a study on this with a bunch of fourth graders while I was a post-doc at The University of Wisconsin-Madison (see full paper below) and the 9 and 10 year olds understood this concept very well after a little instruction.* There is also a very thoughtful summary of the use of average from a history of mathematics perspective by Arthur Bakker of the Freudenthal Institute at Utrecht University. The consensus seems to be that, like any statistic, the average has had many uses over hundreds of years are is neither deceptive nor should it be feared.
At issue during this particular Board of Education debate was simply one member requesting that the district have a goal of decreasing their legal fees by 10%. Legal fees that caused a financial audit violation and are many times higher than the State of New Jersey average. That this request was met by such opposition has both legal and political aspects that space does not allow to fully articulate.
But, as a STEM professor I found the erroneous and misinformed reply of Board member Gold to be worthy of attention and the importance of having a solid background in science and mathematics education and to use it in a thoughtful and professional manner in order to effectively engage in public discourse and debate.
In the end, the Board felt even a 10% reduction of legal fees was too much to consider at this time--a decision seemingly at least influenced somewhat by Mr. Gold's misappropriation of average climatic data and evoking the "deceptive" nature of average argument.
* Petrosino, A. J., Lehrer, R., & Schauble, L. (2003). Structuring Error and Experimental Variation as Distribution in the Fourth Grade. Journa l of Mathematical Thinking and Learning. 5(2&3), 131-156.
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