Reviewed: 
Feb 22, 2007 by Statistics Editorial Board 
Overview: 
This collection of Java applets allows users to explore important ideas in statistics and probability via games and simulation. The eight simulations available are Interactive Scatterplot, Interactive Histogram, Interactive Histogram with Error Graph, Galton Board Game, Monty Hall Game, Red and Black Game, Fourier Game, and Wavelet Game. Each simulation has an About button and an i button which explain the assumptions and directions associated with that applet.
Interactive Scatterplot allows users to create a scatterplot by clicking on the graph to add data points; the applet displays the coordinates of each data point, the regression line and equation, the mean and standard deviation of X and Y, the correlation, and the covariance. Both Interactive Histogram and Interactive Histogram with Error Graph allow users to create a histogram by clicking under the xaxis and to set the number of bins by moving the n slider. The first displays either the mean and standard deviation, median, or boxplot of the data, while the latter displays either the mean square error function or the mean absolute error function.
The Galton Board simulation allows users to choose which way a ball will fall through a triangular array of pegs by clicking the right or left arrow buttons. Monty Hall simulates a game where one of three doors conceals a car; users pick a door, and one of the other doors hiding a goat is opened. Users can then switch to the other unopened door; the applet keeps track of the users decision and the outcome. Red and Black simulates Gambler's Ruin, where the user plays a game until he runs out of money or reaches a target fortune. Users set the parameters, where x is initial wealth, a is the target fortune, v is the amount wagered, and p is the probability of winning a play of the game. The applet keeps track of wins, losses, and number of games played.
The Fourier and Wavelet games allow users to visualize the analysis and synthesis steps in the discrete Fourier transform and the discrete wavelet transform, respectively. This site is a part of the larger Statistics Online Computer Resource (SOCR) available at UCLA. 
Learning Goals: 
The goal of these applets is for students to explore and understand probability and statistical concepts including histograms, scatterplots, regression, and the binomial distribution and to experiment with game simulations in specific contexts. 
Target Student Population: 
This material reaches a wide population of interest. Several applets such as Monty Hall and Interactive Scatterplot are appropriate for high school AP statistics, others such as the Red and Black game are appropriate for undergraduate introductory statistics, while the Fourier and Wavelet games are better suited for more advanced students. 
Prerequisite Knowledge or Skills: 
1) Interactive Scatterplot basic knowledge of the leastsquares line, correlation, and scatterplot;
2) Interactive Histogram & Interactive Histogram with Error Graph basic knowledge of histograms, mean, standard deviation, mean square error, and mean absolute error;
3) Galton Board, Monty Hall, & Red and Black basic probability knowledge;
4) Fourier & Wavelet games discrete Fourier and discrete wavelet transforms, respectively. 
Type of Material: 
Java applet simulations. 
Recommended Uses: 
These simulations could be used as part of classroom demonstrations or in combination with teacher created worksheets or activities in an inquirybased lesson. 
Technical Requirements: 
Internet connection with a Java enabled browser. 
