Exploring Mean, Median, and Mode with a Spreadsheet

To introduce the activities, have the students consider the following problem situation:

An exchange student from Senegal will soon be joining out class.  Before she travels to the United States, she would like to know more about the students she will be meeting.  Unfortunately, she does not read English very well and will not have time to translate letter from each student in the class.  Instead, she would like to receive one letter that describes the typical or 'average' person in the class.

Allow students to brainstorm what types of information they should include and how they might summarize the information.  Ask students to discuss meanings for the term average.

In small groups with about four per group, students should generate written lists of categories describing the kinds of information they would like to gather from their classmates.  They should also describe possible methods of collecting the information, such as survey or by measuring.

Each group should then share it's list with the class which can reach consensus on which categories will be included and how the information should be gathered.

Divide the categories up so that each group is responsible for collecting numerical as well as nonnumeric information.  Try to assign each group at least one category that involves measuring various attributes, such as height, arm span, hand area, etc.  (To measure area of hands and/or feet, students can trace them on centimeter grid paper and count the squares to determine area.)  For categories requiring measurement, assign two or three groups to share data collection for quicker and more efficient gathering.

Allow students to collect all of their data before they begin to enter it into the computer.

You can prepare a spreadsheet template with the headings of the categories the class has chosen and the students names.  This would save time.  But you can also have the students to set this up themselves (remind them to include their units of measure in the column heading, but not in the columns themselves).  An example of a completed worksheet can be found here.

Have students enter their data in each of the columns.

To fill the formulas across the row, select the first cell where the formula is located, move the cursor over the black square in the lower right hand corner of the cell.  When the cursor turns into a skinny black plus sign, you can click and drag to the right.  This copies the contents of that cell over.  When it copies it changes the formula to fit the appropriate column.

Once students have entered all their data, have them save the file and then analyze their data and answer these follow-up questions or questions you come up with yourself.  Experimentation and exploration will help students build relational understanding of key statistical ideas.

Have students use the graphing feature of the spreadsheet to graph the data in their spreadsheet.

Ask the students to use the data and graphs to write a letter to the exchange student describing the 'average' student in the class.

Allow students to graph the nonnumeric data.

Use a scatterplot to show a relationship between two categories, i.e. arm span and height.

If this activity is used as an introduction to types of averages, have students develop the algorithm for the mean.

Explore variations in the data.  For example, in middle school classes there won't be much variation in the ages of the students, but their will in height.