Deadly Blooms and the Intimidating Box-and-Whisker Plot

Last Thursday at The Marine Mammal Center, where I do volunteer care for sick animals, I attended a scientific presentation called “Not All Blooms Are Beautiful—Some Are Downright Deadly!” Much to my surprise, I arrived at an “aha” math moment, but not before learning about how sea lions may lose their sense of smell and how a 9-year-old boy has helped the center advance its research.

California sea lion. (Photo credit: Adam Ratner)

Gregg Langlois from the California Department of Public Health presented data from the last three decades on toxic algae blooms—they are surprisingly frequent, yet human shellfish poisoning is very rare thanks to his efforts to monitor and impose quarantines! And Lauren Di Maio from St. Andrews University presented her research on whether a particular toxin, domoic acid (DA), affects the sense of smell in California sea lions.

Before the presentation began, a boy was introduced who had just celebrated his 9th birthday. He has come to every monthly presentation they’ve had at the Marine Mammal Center, and every year for his birthday, he does a fundraiser to support their work. He’s raised about $1,000!

As the presentation launched, Di Maio started her explanation of the species of microorganisms, and some stuff about the brain receptors that are affected, and about brain chemistry, and the limbic system. . . I was holding onto the gist of it, but definitely missing the finer points. What’s the limbic system again? Why would stimulation of that brain receptor cause a hyperreactive event? And what is a hyperreactive event? (I may be getting all this terminology wrong, I warn you.) I wondered whether the 9 year-old boy, who repeatedly attends these events, was understanding any of this.

Then Di Maio got into explaining how she devised a test to determine whether sea lions can smell (a debated topic among scientists), and compared the results among three groups of sea lions: a control group; a group acutely (short-term) affected by domoic acid toxicosis; and a group chronically (long-term) affected by domoic acid toxicosis. She presented three box-and-whisker plots. Aha! Finally, I was in my element! But not because I’d ever learned box plots in school myself; I learned about them later, when editing math curricula! Here are the plots:

 

What do you glean from this? Di Maio concluded something like, “The control group and acutely DA-affected group of sea lions spent about the same mean time with the fish-scented container, while chronically DA-affected sea lions spent much less time with the scented container. This implies that chronic, but not acute, DA exposure negatively affects the sense of smell, though more research is needed.”

True, the means (the bars in the middle of the boxes) were about the same for control and acute groups. But what about that spread, I wondered? The acute animals had much more spread than the control group. What does that mean? And you may be wondering, what’s the sample size? As I recall, it was n = 25, n = 11, and n = 15, respectively. When I look at a graph like this, I make some conclusions, but it always raises far more questions! Which I guess is exactly what stimulates scientific thinking.

After I left, I talked about the implications of this plot with the friend who had accompanied me. He graduated high school in 2000, a decade later than I, and has a B.S. in computer science. He had never seen a box-and-whisker plot before, though he did assume that it showed something about the spread of data.

As I’m sure was the case for many of you, statistics was not a significant part of my math classes. I surely learned mean, median, and mode, but I don’t recall learning much beyond that in high school, and we didn’t touch statistics in the “pure” mathematics courses I took in college. Somewhere along the line, somehow, I certainly did learn some things about reading and interpreting charts of data. And I’d argue that that’s one of the most valuable things that math education can do for the general population.

This type of statistics has crept into state standards a bit over the last couple of decades. But now, with the Common Core State Standards adopted in about 41 states, we can expect a future where virtually all high school graduates will be able to understand and interpret data like this. I think that’s a very good thing.

For your reference:

An excerpt from the High School Common Core Standards for Statistics & Probability

The Seventh Grade Common Core Standards for Statistics & Probability

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