# Body Measures: Exploring Distributions and Graphs Using Cooperative Learning

This material is replicated on a number of sites as part of the SERC Pedagogic Service Project
Initial Publication Date: November 16, 2006

## Summary

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.

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## Learning Goals

There are four student goals for this lesson:
1. Introduce distributions for univariate data, emphasizing how distributions help us visualize central tendencies and variability.
2. Informally describe distributions in terms of shape, center, and spread.
3. Use technically appropriate language to describe distributions.
4. Consider different sources of variability, including measurement error and individual differences.

## Context for Use

This activity...
• 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

This activity...
• 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
Detailed lesson plan for "Body Measures: Exploring Distributions and Graphs Using Cooperative Learning." (Acrobat (PDF) 93kB Oct13 06)
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

1. 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?
2. Time permitting, this lesson may be concluded by considering the what the following graphs would look like. Consideration of these graphs may also serve as a review activity the day after this lesson is used.
• 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.
3. Throughout the lesson, instructors should encourage students to consider why it is important to describe a distribution. Instructors may also discuss which descriptors can and cannot go together (e.g., normal, skewed, uniform, bimodal, symmetric, etc.)?

Safety Guidelines and Practical Tips:
1. 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:
1. 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.

## Assessment

Cooperative learning requires collective and individual assessments. The absence of either one undermines the cooperative nature of the lesson. Accordingly, the lesson plan emphasizes several ways that instructors may incorporate positive interdependence (i.e., collective assessment) and individual accountability.

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.