MathPlotAI Logo MathPlotAI

Empirical and Theoretical Histograms by Jennifer Loveland

Empirical and Theoretical Histograms by Jennifer Loveland
Loading the math board and drawing, please wait…
2015-03-15 02:41
Probability & StatisticsGraphing
In collections Statistical Applets
This example demonstrates how empirical (experimental) probabilities converge towards theoretical probabilities as the number of trials increases. It involves core math concepts like Probability & Statistics, Histograms, and the Law of Large Numbers. Constructed using GeoGebra commands such as Polygon, Append, TableText, and Histogram. Suitable for high school students learning probability statistics or for educational demonstrations.

GeoGebra Commands & Parameters

  1. Polygon({(1.1, 22), (1.1, 24), (1.5, 24), (1.5, 22)}) → poly1
  2. Polygon({(1.85, 22), (1.85, 24), (2.25, 24), (2.25, 22)}) → poly2
  3. Append("Frequencies", sums) → Tsums
  4. Append("Theoretical Percentage", (thProb * 100)) → TthProb
  5. Append("Actual Percentage", (probs * 100)) → Tprobs
  6. Append("Possible Sums", PossibleSums) → Tpossible
  7. TableText({Tpossible, Tsums, Tprobs, TthProb}, "|_") → text5
  8. Histogram(classes, (probs * 100)) → ExHist
  9. Histogram(classes, (thProb * 100)) → ThHist

AI Drawing Prompt Reference

Create a histogram showing the convergence of experimental probabilities towards theoretical probabilities as the number of trials increases. First, draw two rectangles to represent frequencies in different intervals, then create a table to display the percentages of possible and actual frequencies, and finally, draw histograms for experimental and theoretical probabilities.
The prompt above was compiled from the original drawing commands and is for reference only.