Dr. Andrew Juhl, Columbia University – What Does Average Mean?
In today’s Academic Minute, Dr. Andrew Juhl of Columbia University’s Lamont-Doherty Earth Observatory explains why when it comes to pollution, the extremes are more important than the mean.
Andrew Juhl is an associate research professor at Columbia University’s Lamont-Doherty Earth Observatory. His research is focused on how aquatic microorganisms and their predators interact with each other and their physical/chemical environment. His data on Hudson water quality can be found on the website of the nonprofit group Riverkeeper. He holds a Ph.D. from the Scripps Institution of Oceanography at the University of California San Diego.
Dr. Andrew Juhl – What Does Average Mean?
Dealing properly with natural variability is always a challenge for scientists. Even if you want to measure something simple, like how students at a university scored on the SAT, variability complicates the answer. There is a wide range of scores among any group, so if you wanted to compare one university to another, which scores do you compare? Often in that situation, we calculate the average score. Because the average contains information from all scores, we assume that it represents the group as a whole.
However, sometimes averaging is not the best way to summarize data. For instance, some of my work focuses on the levels of potentially dangerous bacteria found in the Hudson River. For much of the River, if we average together observations during a typical summer, the levels of dangerous bacteria are fairly low, compared to public health guidelines for swimming. That’s good news, and shows the improvement in water quality compared to past decades. But here’s the thing: even though the average may be low, some days the counts at one or another location are very high. That heightens the risk that you could get sick.
Most places are acceptable 70 to 80 percent of the time. Nevertheless, every fourth or fifth sample is unacceptable, sometimes with bacterial levels hundreds of times over the guidelines for swimming. This is particularly common after rain, when runoff overwhelms sewage treatment facilities. Still, this happens rarely enough that ‘average’ conditions in the river are acceptable. The problem is that no one goes swimming ‘on average.’ They go at a particular place, at a particular time. In that context, people want to know: How bad can it get, and under what conditions? Sometimes understanding ‘the extremes’, not ‘the means’, is the best way to deal with natural variability.