So on my first day of doing simple stats things with my freshmen, we focused on them making up their own ways to represent data. The next day, I wanted to continue looking at different representations critically, but also introduce other forms that people already use. Specifically, I had to introduce the ones that the state uses on the MCAS, of course. I had already talked about box-and-whisker plots, and the three I needed to introduce were circle graphs (aka pie charts), histograms (similar to bar graphs), and stem-and-leaf plots. The last representation remaining was scatter plots, which I introduced via a simple project for the break.
Rather than give instructions about how to make each type, I decided to take one collection of data and show three different representations of it. Each thing is fairly straight forward, so I thought I would give students the satisfaction of figuring it out themselves. To make it be data relevant to them, I used the year-to-date grades of students in the class. Once again though, I didn’t do a good job of having kids use the representations to make comments on what the data means.
Here’s the worksheet I made:
*Originally I was going to do this with three different types of data, so that we could see that some representations are better for some data, but this was taking foreverrrr so I gave up on that. I ought to plan ahead more than 1 or 2 days so I have time for this stuff.
*Another note: it didn’t look so sloppy on my work computer. The lines don’t seem to match up in competing versions of word.
I was a little surprised by how much students liked the stem-and-leaf plot, even before they had to choose one of the representations to make on their own. They talked a lot about how they could find the actual mean/median/mode that way, while the other types obscured the data. Very few kids liked the circle graph, since you can’t tell as easily where the high/low scores were. I wish I had another data set to show them an example of how stem-and-leaf plots can fail — such as when you have thousands of numbers.
Here’s how a pair of girls answered the questions:
These are a couple of girls who work super hard all the time, but take longer to build their own big picture. You can see them doing that here, as they point out detail after detail and finally at the end of each section give a summarizing thought.
Students also did a nice job creating their own stem-and-leaf plots, and a decent job with the histograms. They didn’t quite catch on the the historgram x-axis has to be evenly spaced, but that can be built up over time. I’m also confident based even on their imperfect work that they would be able to correctly interpret a histrogram made by somebody else.
Also in case you’re dying to see it, here’s the ‘project’ I assigned for break. I wanted to make something very do-able, since I usually give a decent amount of class-time, but did not this time.
I got real hip and used data about record sales in the US. They’re not fitting any lines or curves to it, just generally talking about the trend. Maybe that’s something I can do later in the year, or with another class.