Lesson 14: Variables, Variables, Variables

Lesson 14: Variables, Variables, Variables

Objective:

Students will learn how to read and interpret multiple variable plots: bivariate scatterplots, multiple variable scatterplots, stacked bar plots, and side-by-side bar plots. They will summarize their learning about multiple variable plots using a four-fold graphic organizer.

Materials:

1. Scatterplot of Heights & Weights handout (LMR_U1_L14_A)

2. Scatterplot of Heights & Weights, Split by Sex handout (LMR_U1_L14_B)

3. Side-by-Side Bar Chart handout (LMR_U1_L14_C)

4. Faceted Histogram of Height by Sex (LMR_U1_L14_D)

5. Summarizing Multi-Variable Plots graphic organizer (LMR_U1_L14_E)

Vocabulary:

scatterplot grouping side-by-side bar plot

Essential Concepts:

Essential Concepts:

To examine whether two (or more) variables are related, we can plot their distributions on the same graph.

Lesson:

1. Begin by informing students that they will learn how to make visual displays using more than one variable, and by asking them to ponder the following questions:

   1. What do you think is the relation between people’s heights and weights?

   2. Are taller people heavier? Always? Or is this just a tendency?

   What do you think is the relation between people's heights and weights? Are taller people heavier? Always? Or is this just a tendency?

   Let's look at some data.

2. Display the following plot to the class (LMR_U1_L14_A) so they can see some actual data:

   
   LMR_U1_L14_A

3. Ask students to individually answer the following questions about the plot on the handout (LMR_U1_L14_A):

   1. What kind of plot is this and how will you remember its features? Answer: Scatterplot. Answers will vary about how students will remember its features.

   2. How many variables are displayed in this plot? Name the variable(s) and identify the type of variable(s). Answer: Two variables. Weight in kilograms and height in meters. Numerical variables.

   3. What do the axes show? Answer: The x-axis shows the height of teens in meters, and the y-axis shows the weight of teens in kilograms.

   4. Do taller people weigh more? Answer: Not necessarily, but there is a tendency for this to be true.

4. Discuss this plot with the class by eliciting students’ responses to the questions. Students actively listen to the discussion by confirming, correcting, or adding to their own responses.

5. Close the discussion by asking students: What questions might you have about this plot? What additional information would be helpful?

6. Now, suppose we could see which of these dots represented girls and which represented boys. Where do you think most of the girls' dots would be relative to the boys?

7. Display the following plot to the class (LMR_U1_L14_B):

   
   LMR_U1_L14_B

8. Ask students to individually answer the following questions about the plot on the handout (LMR_U1_L14_B):

   1. What kind of plot is this and how will you remember its features? Answer: Scatterplot. Answers will vary about how students will remember its features.

   2. How many variables are displayed in this plot? Name the variable(s) and identify the type of variable(s). Answer: Three variables. Weight in kilograms and height in meters are numerical variables. Sex is categorical.

   3. What do the axes show? Answer: The x-axis shows the height of teens in meters, and the y-axis shows the weight of teens in kilograms.

   4. What questions can we ask that this graph might answer? Possible questions are: Who is taller, boys or girls? Who weighs more? Is the association between height and weight the same for boys as it is for girls?

9. Discuss this plot with the class by eliciting students’ responses to the questions. Students actively listen to the discussion by confirming, correcting, or adding to their own responses.

10. Follow-up discussion: when the data are split into categories, it is called grouping.

11. Close the discussion by asking students: What questions might you have about this plot? What additional information would be helpful? Answers will vary.

12. Display the following plot to the class (LMR_U1_L14_C):

    
    LMR_U1_L14_C

13. Ask students to individually answer the following questions on the handout (LMR_U1_L14_C):

    1. What kind of plot is this and how will you remember its features? Answer: Side-by-side bar chart. Answers will vary about how students will remember its features.

    2. How many variables are displayed in this plot? Name the variable(s). Answer: Two variables: whether or not someone is Hispanic, and how often they wear sunscreen.

    3. What are the x-axis and y-axis telling us? Answer: The x-axis shows how often a student wears sunscreen, and the y-axis shows the percentage of the total that fall into that category (broken into two bars, one for Hispanic and one for non-Hispanic).

    4. What statistical investigative questions can you answer with this graph? Possible questions are: Do Hispanics and non- Hispanics have different approaches to sunscreen? What percent of Hispanics always/never wear sunscreen? How does that compare to non-Hispanics?

14. Discuss this plot with the class by eliciting students’ responses to the questions. Students actively listen to the discussion by confirming, correcting, or adding to their own responses.

15. Close the discussion by asking students: What questions might you have about this plot? What additional information would be helpful? Answers will vary.

16. Display the following plot to the class (LMR_U1_L14_D)

    
    LMR_U1_L14_D

17. Ask students to individually answer the following questions on the handout (LMR_U1_L14_D):

    1. What kind of plot is this and how will you remember its features? Answer: Split or faceted histogram. Answers will vary about how students will remember its features.

    2. How many variables are displayed in this plot? Name the variable(s). Answer: Two variables; height and sex.

    3. What are the x-axis and y-axis telling us? Answer: The x-axis shows height in feet, and the y-axis shows the total that fall into a certain range of heights (broken into two histograms, one for males and one for females).

    4. What statistical investigative questions can you answer with this graph? Possible questions are: Do males and females differ in height? What is the typical female height? What is the typical male height?

18. Discuss this plot with the class by eliciting students’ responses to the questions. Students actively listen to the discussion by confirming, correcting, or adding to their own responses.

19. Using the notes and sketches in their DS journals, students will summarize their learning of how to read and interpret basic multiple variable plots by completing the Multiple Variable Plots fourfold graphic organizer (LMR_U1_L14_E):

    
    LMR_U1_L14_E

Class Scribes:

One team of students will give a brief talk to discuss what they think the 3 most important topics of the day were.

Next 2 Days

LAB 1D: Zooming through Data

LAB 1E: What’s the Relationship?

Complete Lab 1D and 1E prior to the Practicum.