# What’s the Average?

Students often answer with the formula: “Add all the numbers together and divide, etc.” with no strong idea of what “average” means. Few adults, in fact, distinguish among the measures of central tendency: mean, median, and mode, but tend to lump them into a general idea of “what’s typical” of the data. Not a bad place to start, but insufficient for understanding the wealth of statistics that overwhelm us in today’s world.

The first activities here immerse students in working with mean, median, and mode both visually and interactively. They will be confronted constantly with the differences among the three concepts of average. The second set offers problems to challenge them to use these statistics in problem situations, such as finding how average temperature changes with distance from the equator.

If you have found a favorite way to help your students understand what “average” is, please share your idea by commenting to this blog post. Thanks!

Describing Data Using Statistics
Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how these statistics change (or, in some cases, how they don’t change).

Understanding Averages
Written for the student, this tutorial on mean, median, and mode includes fact sheets on the most basic concepts, plus practice sheets and a quiz. Key ideas are clearly defined at the student level through graphics as well as text.

Plop It!
Users click to easily and quickly build a bar graph and view how the mean, median, and mode change as entries are added to the graph. An efficient tool for viewing these statistics visually.

Comparing Properties of the Mean and the Median Through the Use of Technology
Seven points appear on a number line, 0 to 400. As students move one or more of these points along the line, the effects on the mean and median are immediately displayed. Questions challenge students to explore these measures of center; for example, What happens if you pull some of the data values way off to one extreme or the other?

Working hours: How much time do teens spend on the job?
This activity challenges students to interpret a bar graph (showing only percentages), to determine the mean number of hours teenagers work per week. A more complicated and interesting problem than it may seem at first glance! A full solution sets out the math in detail. Related questions ask students to calculate averages for additional data sets.

The Global Sun Temperature Project
This web site allows students from around the world to work together to determine how average daily temperatures and hours of sunlight change with distance from the equator. Students learn to collect, organize, and interpret data. Classrooms can participate in the project each spring and each fall. You will find project information, lesson plans, and implementation assistance at the site.

Train Race
In this interactive game, students compute the mean, median, and range of the running times of four trains, then select the one train that will get to the destination on time. Players extend their basic understanding of these statistics as they try to find the most reliable train for the trip. Students can select one of three levels of difficulty. There are tips for students as well as a full explanation of the key instructional ideas underlying the game.

We Want Your Feedback

# Math in Spring and Summer Sports

In the springtime, some middle school students enjoy outdoor sports much more than they enjoy their math classes. Why not use two of these popular sports to our advantage in the classroom? The following problems with baseball and track themes challenge students to exercise some of the skills they learn in the middle school curriculum.

What Is Round, Hard and Sold for \$3 Million?
This activity challenges students to determine which is worth more today: Babe Ruth’s 1927 home-run record-breaking ball or Mark McGwire’s 70th home-run ball that sold in 1999 for \$3 million. Compound interest is the main topic.

Who’s On First Today?
In this activity, students use hits and at-bat statistics to determine which of two baseball players has a better batting average.

Fun with Baseball Stats
In this lesson plan, students use baseball cards to convert statistics to decimals, fractions and percentages. Then, they use their statistics in playing a game. Activity sheets can be downloaded.

Can You Run As Fast As a Car?
This activity asks the student to determine if Florence Griffith-Joyner moved faster than a car traveling 15 miles per hour when she ran 10 meters at a record-breaking 0.91 seconds during the Seoul Olympics. Along with the answer, students will find a description of how to make unit conversions and other problems related to conversions of units of measure for volume, distance, currency, and temperature.

We Want Your Feedback
We want and need your ideas, suggestions, and observations. What
would you like to know more about? What questions have your
students asked? We invite you to share with us and other readers