Speeding Data: Creating and Comparing Box Plots

The purpose of today's class is for students to get some practice constructing box plots and to spend some time working on comparing two sets of data.  My students, many of whom struggle with math and have missed chunks of school in the past, usually need some time to either learn or remember how to make box plots.  I try to use today's lesson as an opportunity for them to get some practice, but also to move forward with the Common Core standards as they compare the spread and distribution of two sets of data.

I begin class by asking students what they think the price of the average speeding ticket is nation wide.  I let students share out their predictions and then share with them some statistics I have found about speeding tickets.  I show them some Driving Citation Statistics from Statistic Brain and we briefly discuss some of the other information presented. 

Next, I let students know that today we are going to look at two data sets that compare the speeds of cars on the northbound and southbound sides of a highway.  We will be looking at the data in box plots to categorize and compare it.

Next, we read through the 1, 2, 3 Speed Trap task together. For this task, I ask students to work alone or in small groups to create their box plots.  This is the first time in my class students will be comparing two box plots, so I may cue them to put them on the same number line (or keep a close eye on their initial plotting efforts).  

Issues I watch for while students work:

• One of set of data has an odd number of speeds and the other is even. I want to make sure students know that for the even set, the two middle numbers go back into the sub median sets.
• I make sure students know they must show the full range of the data on the number line so their scale will need to go from 55 to 83 in this case.
• I'll start to prompt students to compare the differences and similarities between the two data sets. Some of this will happen in the discussion section of the lesson, but I want to get students thinking on their own about how they compare. I might ask them to think specifically about the center, spread, and shape of the data.

Once students have constructed their box plots and written down some comparisons, we'll do a whole class share out. I'll try to elicit from students the main similarities and differences about the data sets.  The main points I want to highlight are:

• The medians of both data sets are the same.  Once students point this out, I ask them what that means. I try to elicit the idea that the "typical" speed on both sides of the highway is the same.
• Students are often confused about how much of the data falls inside of the box.  I want to make sure they know this represents 50% of the data set.  I might ask them then what they think about the two different sizes of the boxes.  What does that mean about the sets of data and how they differ? Students should articulate that more cars on the northbound side drive close to 64mph while on the southbound side, there is more variability in the speeds of the cars.  
• If students don't bring up the point about the symmetry around the median in both boxes, I will try to guide them toward that idea.  The southbound data is symmetric while the northbound side is only slightly skewed left.
• We also spend some time talking about the outlier in the northbound side of the data.  I ask students what the data would look like if the 83mph speed was removed.  

Because box plots may be new to my students, I also want to touch on some of the basics about the range, quartiles, IQR, etc.  

I finish today's class with a 3-2-1 Reflection about Box Plots.  I ask students to write down:

• 3 things they learned today
• 2 ways this connects with something we've learned in the past
• 1 question they still have.