GO IN DEPTH

# The One in the Middle

#### Materials

• Post-It notes ### Purpose

To review and reinforce the concepts of mean, median, and mode.

### Context

By the end of the 5th grade, students should have begun to explore data in rather formal ways. As stated in Benchmarks, “The questions about data only explored in the earliest grades can now be made into formal questions. Data distributions should be made of many familiar features and quantities: heights, weights, number of siblings, or kinds of pets. The important thing to emphasize at this level is the kind of questions that can be posed and answered by a data distribution: 'Where is the middle?’ is a useful question; ‘What is the average?’ probably is not.” (Benchmarks for Science Literacy, p. 227.)

At the 6-8 level, students can build on what they learned in earlier grades to develop an understanding of concepts such as mean, median, and mode. “Research suggests that a good notion of representativeness may be a prerequisite to grasping the definitions for measures like mean, median, or mode. Students can acquire notions of representativeness after they start seeing data sets as entities to be described and summarized rather than as ‘unconnected’ individual values. This occurs typically around 4th grade." (Benchmarks for Science Literacy, p. 354.)

This lesson provides simple activities to review and reinforce mean, median, and mode. It is intended to supplement other instruction on these topics, both in science and mathematics classes. As the Benchmarks states, “Students should make distributions for many data sets, their own and published sets, which have already inspired some meaningful questions. The idea of a middle to a data set should be well motivated – say, by asking for a simple way to compare two groups – and various kinds of middle should be considered.” (Benchmarks for Science Literacy, p. 228.)

Note: See the Science NetLinks lesson What Can Data Tell Us? for a prerequisite lesson that addresses data distribution.

### Motivation

Ask students to describe how math and science are dependent on each other. How is math used in this science class? How are math and science interwoven in real life?

Tell students that today will be a review of mean, median, and mode. Have students describe what they know about these terms already.

### Development

This section of the lesson provides simple, participatory activities that help reinforce the concepts of median, mean, and mode. All of the activities make use of the number of siblings of the students.

Median and Mode
Have each student record the number of brothers and sisters they have (the total number of brothers and sisters combined) on a Post-It note. Have the class physically organize the Post-It notes into a graph.

Help students interpret the data by asking questions such as:

• What is the range of the data? That is, what are the highest and lowest numbers?
• Are there places with no data?
• Are there places where the data are clumped?
• What is the typical number of siblings?

Ask students to determine the median and mode of the data. Review the definitions of these terms as necessary (in language appropriate for your students):

Median: the middle of the data set
Mode: the value or category that occurs most frequently in the data set; the value most frequently reported

The following activities allow students to see the median in a different way. Have students arrange themselves side-by-side in the room according to the number of brothers and sisters each has. Students with the same number stand next to each other. Have students call out their number and record this information (in a horizontal row from left to right) on the board or a large piece of paper. For example, 0,0,0,1,1,3,3,4,4, etc.

Now tell the students that you will find the middle value (or median) of all the numbers called out (arranged from the smallest to the largest). To do this, have a pair of students on each end sit down. Continue having pairs (one from each end of those standing) sit down. If one person is left standing, his/her number is the median value. If two students are standing, the average of the two numbers is the median value.

Finally, verify the results with the numbers you have written on the board or on the large piece of paper, crossing out pairs from each end until you are left with only one or two numbers.

Mean
Review with students the definition of mean, as necessary (in language appropriate for your students): the average determined by adding the numbers of a set, then dividing the sum by the number of numbers added.

Have students calculate the average value (or mean) by adding the total number of siblings and divide it by the number of students.

### Assessment

Help students compare the mean, median, and mode values by asking questions such as:

• What do each of these values tell you about the middle of the data set?
• How are these values similar? How are they different?
• How would you describe the mean to a younger student? The median? The mode?
• Why do you think barriers in highways are called medians?

Ask students to describe another data set for which they could identify mean, median, and mode.

Finally, have students describe how mean, median, and mode values are useful in everyday life. Have them think about situations such as grade averages, sports, and weather.

### Extensions

For other activities on mean, median, and mode, see the following sites:

The MMMR Rap is a rap that a teacher created to help students remember the concepts of mean, median, mode, and range.

Have students visit a weather site such as The Weather Channel to see how these values are useful in reporting weather. You could invite a local weather person to your classroom to discuss the role of data in weather reporting.  