Using Box Plots to Investigate Data

Subject: Mathematics

Grades: 8-12
Ages: 13-18

 

Lesson Objective

In this lesson, students will use movie data to look for connections between a film's length, ratings and the type of recognition it has received.  Using Box plots, students will investigate the distribution of movie lengths and the impact of other variables on that distribution.  They will gain a deeper understanding of the 5-number summary and learn how to use quantities to describe data.    

 

Teacher Instructions

       1. Take an informal class survey.  Some potential questions are:  On average, are movies that win Academy Awards longer, shorter or the same length as movies that don't win Academy Awards?  On average, which movies are longer in length - those rate G, PG, PG-13, or R?  On average, which movies have the largest range of length - those rated G, PG, PG-13, or R?   
 

2. Open the    Movies database:  InspireData Starter>Databases>Mathematics>Movies.  Discuss the contents of the table, including the field notes for Recognition Type.

 

 

3. As a demonstratio  n, switch to Plot View and create an Axis plot for the distribution of movie lengths.  Add a Box plot by selecting Box Plot from the Plot menu.  Add numeric labels to the plot by checking Add numeric labels to box plots under Box Plot Options.

 

 

 

4. Lead a class discussion on the interpretation of Box plots and how to use them to describe the distribution of a set of data in the context of a real w  orld situation.  For example, using the Box plot above we could say:  "Fifty percent of the  movies were less than 124 minutes in length."  Be sure to include a discussion of the whisker length.  What does it mean if we notice that whiskers are short in comparison to the box?  Or vice versa?  Does our data show that one whisker is longer than the other?  What does that mean about movie lengths?  Demonstrate how to use the Notes area and create a slide by using the Capture Slide button in the Slide Sorter.
 

5. Divide students into as many groups as there are computers available and direct them to answer the questions below using Box plots.  For each plot, have students summarize their findings in the Notes area and capture a slide.  (Optional:  Ask students to include obs  ervations involving percentages.)
 

• How are movie lengths distributed?
• Is there a relationship between a movie's length and its ratings?
• Is there a relationship between a movie's length and its type of recognition (Oscar winner, box office hit or unpopular with viewers)?

(Note: The first question will require students to re-create the Box plot that was demonstrated and add their own analysis. The second and third questions will require students to make multiple Box plots by setting the Y axis to either Recognition Type or Rating.)

 

 

6. Reconvene the class and assign a group or multiple groups to present their slides to the class.  For each slide, ask for additional observations from i  ndividual students.  Discuss how Box plots inform answers to the initial survey questions in Step 1.

Assessment

• An informal assessment of how well students understnad Box plots and use them to describe a set of data in a real-world context can be done during class demonstrations and discussions.
• Plots and written observations can be turned in or assessed during the presentation.

Adaptations

• If students have experience with describing the distribution of data (uniform, normal, skewed left, skewed right), have them use the terms to describe each distribution from the Box plot and then examine Stack plots or Bar charts to confirm answers. 

 

 

• Have students add data from their favorite movies to the database. Data can be entered directly or by using the Survey or e-Survey tools.
• Have students choose another area of interest, conduct research to collect data and use Box plots to interpret their data set.