Box Plots and Interquartile Range
Lesson 15 of 22
Objective: SWBAT: • Identify and label the minimum, maximum, lower quartile, upper quartile, and median of a data set and box plot. • Define and identify interquartile range. • Analyze and compare box plots.
See my Do Now in my Strategy folder that explains my beginning of class routines.
Often, I create do nows that have problems that connect to the task that students will be working on that day. Today I want students to analyze a line graph in order to answer questions. Each edition of Scholastic DynaMath typically includes a graphs in each edition.
I ask for students to share their thinking. Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.
I introduce the problem to students. I want students to apply what they already know about box plots from the previous lesson. Students participate in a Think Write Pair Share. I walk around and monitor student progress as they work.
I call on students to share out their ideas. I push students to support their idea with data from the set. I want students to notice that although Thaisha and Thaima have the same median about of money earned, their data sets are not identical. I also want students to notice that the size of the box is different for each box plot. If this comes up, I ask students what they think this tells us about the data sets. Students are engaging in MP3: Construct viable arguments and critique the reasoning of others and MP2: Reason abstractly and quantitatively.
I call on students to read and fill in the definitions for the measures of center. I explain the difference between measures of center and measures of variability. I introduce the concept of interquartile range. We work together to calculate each measure for Thaisha and Thaima’s box plots. I want students to see that the box in Thaima’s box plot is longer, which means that the middle 50% of her earnings are spread between $84 and $94. Thaisha’s box is shorter, and her middle 50% of her earnings are spread between $85 and $90.
Creating a Box Plot
We work together to use the data set to create a box plot. A common mistake is for students to immediately start to find the median of the data set without reordering the values from least to greatest. I start to make this mistake and ask students if they agree or disagree with my action and why.
For the last two questions, students participate in a Think Write Pair Share. I want students to be able to explain that the IQR shows the range of the middle 50% of the data. Even though the range of the entire team is 9 inches, the range for the middle ½ of the players on the team is 3 inches.
- Before this lesson, I use the tickets to go from the previous lessons to Create Homogeneous Groups of 3-4 students.
- I also use the ticket to go data to determine which practice page each group should start on.
- I create and Post a Key around the room.
- I copy a Group Work Rubric for each group.
I review expectations and students move into groups. I tell groups which practice page to start on. Different groups will work through the practice pages at a different pace. My goal is that I have grouped students so that they are working at a similar level for these practice problems. Students are engaging in MP1: Make sense of problems and persevere, MP2: Reason abstractly and quantitatively, and MP3: Construct viable arguments and critique the reasoning of others.
As students work, I walk around and monitor student progress and behavior. If a group of students complete a page, I quickly scan their work. If they are on track, I send them to check their work with the key. If students are struggling, I may ask them one of the following questions:
- What is the question asking?
- What does this point represent?
- What is does this part of the box plot tell us? How do you know?
- What is a quartile?
If students complete the questions they can work on the challenge problems.
Closure and Ticket to Go
I ask students to flip to the closure problem. I ask students how the weekly hours compares between Sarah and DeShawn. I explain that they need to write 5 observations by analyzing the box plots. I also want them to think about the two other questions about IQR.
Students participate in a Think Pair Share. Students are engaging in MP2: Reason abstractly and quantitatively and MP3: Construct a viable argument and critique the reasoning of others.
I call on students to share out their observations. I push students to use accurate language and to use the box plot to support their observation. I want students to recognize that the IQR for DeShawn’s weekly hours is smaller than the IQR for Sarah’s hours. This means that the middle ½ of Shawn’s weekly hours have a range of 4 hours. Sarah’s IQR is larger because the middle ½ of her weekly hours have a range of 8 hours. I want students to see that Sarah’s data is symmetric and DeShawn’s data is skewed. Students are engaging in MP6: Attend to precision.
I pass out the Ticket to Go and the Homework.