Statistics: Center of Mass

Objectives

• Students will identify and interpret the mean geometrically as the location such that the sum of the distances on either side of the mean is the same.
• Students will recognize that the center of balance for a set of univariate data is the weighted mean.

Vocabulary

• centroid
• maximum
• center of balance
• minimum
• fulcrum
• range
• mean
• median
• weighted mean

About the Lesson

This lesson involves locating the point along a 12-inch ruler that will balance five quarters taped to various locations.
As a result, students will:

• Drag the fulcrum on the ruler and observe that the point that balances the arrangement will be the position in which the sum of the moments, or the product of the Force (F) and the distance (d) from the fulcrum, is equal on each side of the fulcrum.
• Identify the center of balance (or the center of mass) as the point where the sums of the distances on each side of the fulcrum are equal.
• Discover the physical balance point is associated with the arithmetic mean of the numerical locations of the quarters.