# Analyzing a Box Plot

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## Objective

SWBAT interpret data using the shape of a box plot and compare data sets using box plots.

#### Big Idea

Students use real life data to construct box plots while gaining conceptual understanding of how the shape of a distribution tells a story.

## Opening

10 minutes

Today I provide two warmup problems to help open the class. For the problem on Slide 2 of box_plot_day3, students work individually at first and then collaborate with their partner. After a few minutes, I will have 1 or 2 students read their explanation. I will ask others to offer ideas about how to improve the explanation, or, name something that they like about the explanation.

As I observe and listen to the students' work on this first problem, I am trying to determine if students can visualize how a box plot serves to divide up the data into four equal sections.  Without having any concrete data to work with, students need to determine where the center of a data set of 25 would lie.

Teaching Point: some concrete learners struggle with these types of questions.  I encourage students who are struggling to draw 25 vertical lines (to help with visualizing) and then find the center.  You can also have students write down the numbers 1, 2, 3 ,4, 5 and 1, 2, 3 4 to compare where the center falls for both an odd and even data set.  They can then generalize this understanding to a data set of 25.

We explore the problem on Slide 3 using the same methods as in Slide #2.  I use this question to review the vocabulary we use when working with box plots.  To do this, I draw a box plot on the board and go through the vocabulary one location at a time.  I call on students to offer as many different ways to refer to the same location as possible.

## Investigation

30 minutes

Students work on both tasks on the Stats_Box_Plot handout collaboratively with a partner.  I encourage students to talk out the answers they are going to record on paper. I say, "discuss the analysis questions with your partner before writing anything to ensure that it sounds smart."  I use this term frequently to try to raise the level of discourse and writing in my classroom.  Many students will write analyses that are very surface level. By pushing them to become more analytical and descriptive, I think I can help my students to think and to understand more deeply.

When describing statistical graphs, students can use an "I noticed that _________________ because _________________" sentence structure to record their idea.  I provide a template for them to think with because it helps students to frame their thinking. It is important to continually remind students to back up their observations with evidence.

## Closure

5 minutes

The ticket out the door is on Page 4 of Box_Plot_Day3. I will ask students to choose one of the two statements to speak to.  They will answer this question individually and submit their answer to me at the end of the class.  By judging the level of sophistication in what students are explaining or questioning, I can get a good sense of the level of understanding that the students have.