Estimating Proportions from Samples: Visualizing Sampling Variability

This example demonstrates how an estimated proportion changes when repeatedly sampling from a population: the sample proportion fluctuates around the true (target) proportion, and the variability becomes visible through a constructed scatter-plot style visualization. Key mathematical ideas include probability and statistics concepts such as proportions in Bernoulli/binomial-type sampling, the role of sample size n, success counts versus sample proportions, and the inherent randomness of estimation from samples. Construction-wise, the GeoGebra setup uses the Shuffle command to randomly rearrange sample elements; it then updates plotted objects and annotations using data/index objects (e.g., n, A, B, C, D, i, j) together with interface elements like the scene (pic1), buttons (button1/button2/button3), and text labels (text3/text4/text5/text6). The geometry and symmetry-like layout help learners track how the computed proportion corresponds to the current sample configuration. Suitable for secondary school advanced learners through introductory university probability/statistics, especially for interactive classroom demonstrations and conceptual practice.