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Using Stats with Your Students: Frequency Distribution Histograms

How do you make restoration data in a spreadsheet tangible for students?  We looked at one approach- building a histogram using index cards- in our professional development, Using Stats with Your Students.
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As a part of the Billion Oyster Project, students all over New York City monitor Oyster Restoration Stations (ORS) and upload the data they collect to the BOP Digital Platform.  Students measure oyster growth, record site conditions, note the presence of sessile and mobile organisms, and conduct water quality testing.  Here at BOP, we can use this valuable data to inform our future restoration efforts- but it’s also a powerful classroom tool to teach data analysis and statistics concepts.  And it’s especially important for students who are presenting original research projects in the Third Annual BOP Research Symposium, who can study other schools’ data in addition to their own to investigate what fascinates them in New York Harbor.

Middle school students are definitely capable of making sense of this data, but it can certainly be overwhelming for them at first!  To help support their students, BOP teachers worked with BOP Curriculum Specialists Annie Lederberg and Ann Fraioli at a recent professional development, Using Stats with Your Students.  Annie and Ann guided teachers through the process of extracting useful data from the Digital Platform, cleaning it up, and creating a tangible visualization of it via an index card frequency distribution histogram.  In this post, we’ll take a closer look at the index card histograms, but first, here are two earlier posts you might want to check out:

  1. How to Work with Data from the Digital Platform” is a step-by-step guide, with screenshots, to downloading data from the BOP Digital Platform and cleaning it up in Excel.  It’s meant to be student-friendly, so it’s useful for any folks who might need a refresher on how to work with Excel.
  2. Getting the Right Environmental Data into the Classroom” is a set of tips on how to look at Digital Platform data from a PD held by our partners at Columbia University, Professors Bob Newton and Matt Palmer.  This post includes basic steps to take when examining the data (like checking the method and units, doing a Google search for a quick comparison, keeping mindful of user error, etc.) and an excellent list of data sources to compare Digital Platform data to, like the Jamaica Bay Water Quality Data Visualization and Access Tool.  (If you’re interested in learning more from Bob and Matt, sign up for Part 2 of this PD, “Figuring out what environmental data are telling us” on April 24th!)

At Using Stats with Your Students, Ann and Annie focused on oyster measurement data from two ORS monitoring expeditions conducted by citizen scientist Andrea Bearbower.  During each expedition, students and citizen scientists pull out 10 tagged shells from the ORS:

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Tagged and untagged oyster shells in an Oyster Restoration Station.

…and then they count how many live oysters are attached to that tagged oyster shell and measure each one using calipers:

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When you pull this data from the Digital Platform and clean it up, you might get something like this in Excel:

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In the “Measurements” row above, the measurements of each live oyster attached to substrate shell #1 appear in one cell.  There are a few different approaches you could take to visualizing this data, but teachers and students first have to decide what they want to know.  Would you average all of the values together, giving you an average live oyster size per shell?  Or maybe you would average all the oyster measurements from all the shells, to come up with an average live oyster size for each expedition, so you could see the change in size over time?

That’s certainly one valid option, and it’s a metric we at BOP use in our own restoration work.  However, a drawback to this approach is that it hides the variation in sizes you might see in your oyster population on each expedition.  If you want to capture this diversity, you might want to try out a frequency distribution histogram.  This kind of graph helps students visualize how many oysters fit into a selection of size ranges.

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Cohort 3 BOP-CCERS fellow Jennifer Carpenter of PS 369K shows off a frequency distribution histogram of oyster measurements she sketched during the PD.

A frequency distribution histogram asks students to:

  1. Make a decision about how to group a range of numbers.  (For example, if the oyster measurements range from 10mm to 75mm, do you create groups like “10-15mm” or “10-20mm?”)
  2. Count how many oysters fit into each group.

 

At the PD, teachers tried out a hands-on activity they could use with their students to help them build a histogram, piece by piece, by representing each oyster’s measurement on one index card.  First, they were given a sheet of paper with a set of rulers on it.  They then had to highlight each oyster’s measurement from the two expeditions on the rulers, labeling them by size and using a different color for each expedition:

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The teachers then cut each measurement out and taped it to an individual index card.  This activity works with any size/type of paper as long as they’re all equally sized- Annie brought in samples taped to paper cut into equal squares:

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Teachers then had to decide on groupings and place each individual card along an invisible x and y axis on their tables, building the frequency distribution histogram:

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Histograms can be used with other data from the Digital Platform too- Annie and Ann included the one below in the PD materials.  This one looks at all the expeditions on the platform, and shows the distribution in dissolved oxygen levels:

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Where do you go from here?  After taking a close look at the Digital Platform data, the BOP Curriculum Team recommends comparing it to another source to contextualize it- for example, one of the sources from Bob and Matt’s list here.  And of course, it’s always great to follow what piques your students’ interest as you go along!  Maybe they’ll want to take a look at other New York Harbor data, or data from other US ports, or data from the open ocean, or the Antarctic?

If you’re interested in more professional developments like this, we hope you’ll join us- click here to see all upcoming events and sign up on the BOP Digital Platform!

Posted 4/3/17 at 6:38 PM