Finding the Mean or the Average

The concept of average is at one level an obvious concept. At another level, few students see how average "levels out" variation in the data. It can be used as a standard or measure to make judgements about the data. For example, it is the best predictor of a new piece of information.

In this exercise, students will be able to work with a simple set of scores. They will use the spreadsheet to compute the average, then create a chart showing 5 scores and the average. As a final way of communicating how the average "levels out" the data, they will manipulate arrays so that they are all the same height.

Classroom Discussion and Activities

Computer Lab Activities

Classroom Discussion and Activities (Whole Group or Teams)

You can use any variety of data to introduce the concept of average. It is important, however, that you begin with a relative small set of numbers and that the numbers aren't too large. In the introductory lesson, your average should be a whole number. You can model averaging in class by using a transparency that is divided up into grids. It could look like the arrays below. Another option is to use stacking blocks or have the students use graph paper and colored pens.

Begin with a set of columns as shown in the table below. Create a column that represents the average. You can then show how all of the columns can be "adjusted" to the same height as the average. This should lead to a discussion of the concept of average. Again, it can be useful to have students manipulate the numbers and divide to find the average as well as represent this concept using graph paper. In the end, students should be able to explain that averaging "levels off" or flattens the variation in numbers.

 

In the Lab (Individual or Paired Work)

• Open the file average.xls. This file has two important pieces of information. First, there are five scores in the upper left corner. Second, the scores have been arranged as columns or arrays down below.

• Start with the five scores. Have the students compute the average. The formula is =average(B2:B6).

• Have the students create a bar chart of the five scores and the average. Be sure to discuss how the average column in the bar chart provides a standard against which all of the other scores can be compared. Remind students of the classroom discussion of how the average "levels off" all of the other data.

• Have students create and color an array that represents the average. In this example, that number will be 12. They should have a colored and bordered column that is 12 cells high.

• Finally, have the students drag the cells in the other arrays so that they are all the same height as the average column. Be sure to discuss averaging in the context of this display, and relate this to the bar chart that they have created in the space above.