In this post I’ll be telling a tale of averages gone wrong. I tell it not just to describe the circumstances but also as a mini-exercise in quantitative literacy (numeracy), which is as much about critical thinking as it is about numbers. So if you’re game for some quantitative calisthenics, I believe you’ll find this tale invigorating. Also, you’ll see examples of how simple, unadorned statistical graphs are indispensable in data sleuthing!
Let me begin, though, with a complaint. I think we’ve all been trained to trust averages too much. Early in our school years we acquiesced to the idea of an average of test scores being the fairest reflection of our performance. Later in college statistics courses we learned about a host of theories and formulas that depend on the sacrosanct statistical mean/average. All of this has convinced us that averages are a part of the natural order of things.
But the truth is that idea of averageness is a statistical invention, or more accurately, a sociopolitical convention.1 There are no such things as an average student, average musician, average automobile, average university, average library, average book, or an average anything. The residents of Lake Wobegon realized this a long time ago!
Occasionally our high comfort level with averages allows them to be conduits for wrong information. Such was the case for the average that went wrong found in this table from a Public Library Funding and Technology Access Study (PLFTAS) report:
Source: Hoffman, J. et al. 2012, Libraries Connect Communities: Public Library
Funding & Technology Study 2011-2012, 11. Click to see larger image.
The highlighted percentage for 2009-2010 is wrong. It is impossible for public libraries nationwide to have, on average, lost 42% of their funding in a single year. [Read more…]
1 Desrosières, A. 1998. The Politics of Large Numbers: A History of Statistical Reasoning. Cambridge MA: Harvard University Press. See chapters 2 & 3.