Broken Wand: Geometric Construction to Explore Mean, Variance, and Mode

This GeoGebra example demonstrates how a “broken” geometric arrangement can be used as a visual scaffold to study statistical characteristics. By placing and connecting a sequence of points into segments, the model supports forming data-like collections and then relating them to key summary measures. The main mathematical concepts include combinatorics (building possible value sets), arithmetic mean, variance, and mode—quantities that describe central tendency and spread. Construction-wise, the provided summary indicates the core GeoGebra commands are Point and Segment: it creates point objects A, B, f, C, g, D, h, E, i and links selected points with segments to form the broken-wand geometry. The resulting figure is suitable for middle and high school learners, classroom demonstrations, and self-study on combining geometric construction with basic probability & statistics reasoning.