**ERIC Number:**EJ993617

**Record Type:**Journal

**Publication Date:**2012-Oct

**Pages:**8

**Abstractor:**ERIC

**ISBN:**N/A

**ISSN:**ISSN-1072-0839

The Mean as Balance Point

O'Dell, Robin S.

Mathematics Teaching in the Middle School, v18 n3 p148-155 Oct 2012

There are two primary interpretations of the mean: as a leveler of data (Uccellini 1996, pp. 113-114) and as a balance point of a data set. Typically, both interpretations of the mean are ignored in elementary school and middle school curricula. They are replaced with a rote emphasis on calculation using the standard algorithm. When students are asked why the mean is an important number descriptor of a data set, they typically respond, "because it uses all of the numbers when you calculate it." They rarely demonstrate any conceptual understanding of the term or its properties. The activity in this article is a student-centered sequence of tasks that develops the interpretation of the mean as the balance point of a set of data. It also allows students to discover the following characteristics: (1) The mean is a value located between the maximum and minimum values of the data set; (2) The mean does not have to be a member of the data set; and (3) For any data set, the sum of the signed distances of numbers from the mean of the data set is zero. The activity has two parts. First, students work through a sequence of hands-on tasks requiring them to balance a set of cubes on a ruler-and-fulcrum seesaw. These actions are equivalent to constructing data sets, each with a mean of 6, and require students to consider each data point's distance from the mean. Ideas developed during this pursuit are then used in the second part of the activity when students determine the mean of small data sets. This sequence of tasks can be completed within one extended period or two typical class periods. (Contains 6 figures.)

Descriptors: Middle School Students, Mathematics Instruction, Mathematics Education, Mathematics, Computation, Mathematical Concepts, Numbers

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**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A