Skip to content

Mean as Balance Point

Run the Mean as Balance Point MicroSim Fullscreen

Edit this MicroSim in the p5.js Editor

About This MicroSim

This interactive visualization helps students understand that the mean represents the balance point of a distribution. Just like weights on a seesaw, data points exert "torque" around the mean, and the mean is the unique position where these forces balance.

How to Use

  • Drag data points left or right to see the mean update in real-time
  • Click on the number line to add new data points
  • Double-click a point to remove it
  • Toggle Show Calculation to see the sum and division

Key Insights

  1. Moving a point farther from the center causes a larger shift in the mean
  2. Adding an extreme value dramatically shifts the balance point
  3. The beam tilts toward the "heavier" side until the fulcrum is at the mean
  4. The mean is sensitive to outliers - one extreme value can pull it significantly

Lesson Plan

Learning Objective

Students will understand that the mean represents the balance point of a distribution by manipulating data points and observing how the mean shifts in response (Bloom's Taxonomy: Understanding).

Activities

  1. Exploration (5 min): Let students freely manipulate points to develop intuition
  2. Prediction (5 min): Before moving a point, ask students to predict which direction the mean will shift
  3. Outlier Investigation (5 min): Add an extreme value (like 95) and observe the dramatic shift
  4. Discussion: Why is the median sometimes preferred over the mean?

Assessment Questions

  1. If all data points are at the same location, where is the mean?
  2. What happens to the mean when you add a point at 0? At 100?
  3. If you have points at 20, 30, 40, and 50, where should you add a fifth point to make the mean exactly 40?

References