Reasoning About Center and Spread: How do Students Spend Their Time?

This page is authored by Shirley J. Alt, based on an original activity by Joan Garfield and Robert delMas. Alt, Garfield, and delMas are all at the University of Minnesota, Twin Cities. The original activity was written and described in Garfield, delMas & Chance (in press).

Author Profile

This activity has been undergone anonymous peer review.

This activity was anonymously reviewed by educators with appropriate statistics background according to the CAUSE review criteria for its pedagogic collection.

This page first made public: Apr 5, 2007

This material is replicated on a number of sites as part of the SERC Pedagogic Service Project


This activity is designed to develop student reasoning about variability in data sets by having them make predictions about the average number of minutes (in a 24 hour period) they spend traveling to and from school, exercising, eating, studying, and talking on the cell phone.

The students predict which of these daily activities will have a lot and which will have a little variation. Then the students examine their choices through the use of computer software. The final task in the activity has the students use reasoning about distributions to examine graphs and summary statistics from real world data to choose variables that have a lot and have a little variability.

Learning Goals

To promote student reasoning about center and spread through the use of conjectures, computers and real world data.

Context for Use

This activity is usually done at the end of a unit on descriptive statistics in an entry level statistics course. The lesson takes approximately 75 minutes and is well suited to any size classroom. The activity may easily be adapted for junior high, high school, and college-level instruction.

Description and Teaching Materials

The students will use graphs and statistics to reason about center and spread. Further, they will test their conjectures about the amount of time students spend traveling to school or exercising in a week by first making predictions and then testing these predictions against real world data.

This activity asks questions to promote student reasoning about center and spread and has the students use graphs and statistics to analyze their student daily time data. The worksheet for reasoning about center and spread consists of having the students make predictions about the amount of the time the students in their class spend: traveling to school, exercising in a week, communicating with their parents, eating, on the internet, studying, and on their cell phones.

Instructor Lesson Plan

This lesson builds ideas of variability in distributions, tying together the concepts of shape, center and spread.

Goals for the Lesson:

Materials Needed:

How to Guide Students to Make and Conjectures

The Process of Having Students Make and Test Conjectures

Teaching Notes and Tips

Time Involved:

Helpful Hints:

Be sure to ask students to share their predictions and reasoning first in small groups, then with the entire class. Ask probing questions such as, why did you think that. Ask representatives from different groups to report on their results.

For more tips on using cooperative groups, see the Cooperative Learning Module.


References and Resources

Garfield, J., delMas, R., and Chance, B. (in press). Using student informal notions of variability to develop an understanding of formal measures of variability. In Thinking about Data, edited by P. Shah and M. Lovett.