Empirical vs Theoretical Histograms: Convergence with Increasing Trials

① This GeoGebra example dynamically demonstrates how empirical (experimental) histograms converge to theoretical histograms as the number of trials (dice rolls) increases. ② Core mathematical concepts include frequency vs probability, the law of large numbers, histogram representation, and the distribution of discrete random variables (e.g., sum of two dice). ③ Construction details: Uses GeoGebra commands such as Polygon, Append, TableText, and Histogram; objects include s2 through s12 (frequencies for each sum), sums, Rolls, probs, button1 (roll button), classes, thProb (theoretical probabilities), PossibleSums, text1, button2, A-H, poly1, poly2, d1, text2, d2, text3, button3, button4, Tsums, TthProb, Tprobs, and Tpossible. Buttons control the number of trials and dynamically update the graphs. ④ Suitable for high school or college probability/statistics courses to illustrate the law of large numbers and the stabilization of relative frequencies, and for mathematical experiments or inquiry-based learning.