Body Measures: Exploring Distributions and Graphs Using Cooperative Learning
This material was originally developed through CAUSE
as part of its collaboration with the SERC Pedagogic Service.
Using cooperative learning methods, this lesson introduces distributions for univariate data, emphasizing how distributions help us visualize central tendencies and variability. Students collect real data on head circumference and hand span, then describe the distributions in terms of shape, center, and spread. The lesson moves from informal to more technically appropriate descriptions of distributions.
- Introduce distributions for univariate data, emphasizing how distributions help us visualize central tendencies and variability.
- Informally describe distributions in terms of shape, center, and spread.
- Use technically appropriate language to describe distributions.
- Consider different sources of variability, including measurement error and individual differences.
Context for Use
- Is appropriate for the beginning of an introductory statistics course.
- May be adapted for junior high, high school, and college-level instruction.
- Is most effective with class sizes of 15 or more students.
- Lasts 50 - 75 minutes.
- Can be easily adapted to emphasize (1) sources of variability, (2) measurement protocols, (3) mean difference and regression analyses.
Description and Teaching Materials
- Assumes that students are familiar with data entry and a statistical software program (e.g., Excel, Fathom, SPSS, Minitab, etc.).
- Uses materials: (1) tape measures, (2) statistical software
Student activity sheet: Head Circumference CL (Acrobat (PDF) 18kB Oct12 06)
Student activity sheet: Hand Span CL (Acrobat (PDF) 17kB Oct12 06)
Student activity sheet: Body Measures Group CL (Acrobat (PDF) 16kB Jun30 06)
Teaching Notes and Tips
- We encourage instructors to begin this lesson with a "hook"—questions that make the lesson relevant, fun, and intriguing. Sample questions include:
- Are college students all the same?
- Are students enrolled in this course pretty similar?
- Do some statistics students have bigger heads than others?
- Do some statistics students have bigger hands than others?
- Salaries of all persons employed at this at this school (university, etc.).
- Grades on an easy test.
- Grades on a difficult test.
- Amount of times freshmen students study the first week of class.
- Age of cars on a used-car lot.
- Amount of time spent by student on a difficult test in a 50 minute class.
Safety Guidelines and Practical Tips:
- Encourage students to measure head circumference of a seated student. Often, sitting makes measurement easier and less awkward, especially for those students who are not as tall as their partners.
Making the Best Use of This Activity:
- One of the most powerful aspects of this lesson is differentiating between measurement error and individual differences on a given attribute. To do this, as many different students as possible should measure the instructor (or a designated student's) head circumference and hand span. The instructor then graphs this data for the entire class. In our experience, this illustration prompts a lively discussion about sources of variability, measurement error, potential test bias, etc.
In this lesson, we recommend that every individual student is responsible for presenting data analytic results, and awarding bonus points for successfully completing the group worksheet.
References and Resources
CAUSEweb includes other interesting activities for exploring distributions and graphs: http://www.causeweb.org/repository/StarLibrary/activities/