Central Limit Theorem A Demonstration of SOCR This paper is a joint work with my colleagues Ivo Dinov (Director) and Juana Sanchez. SOCR stands for Statistic Online Computational Resources and it is a free ware funded by the NSF and it is in its 5th year of development. It’s Online, Therefore It Exists! Nicolas Christou and Ivo D. Dinov UCLA Department of Statistics www.SOCR.ucla.edu MERLOT International Conference New Orleans, Louisiana August 9, 2007

Outline What is SOCR? How to access SOCR Components of SOCR It is a collection of interactive applets aim to assist students, educators and developers in the teaching of probability and statistics. It can be accessed at socr.ucla.edu. What is SOCR? How to access SOCR Components of SOCR Distributions Experiments (CLT) Activities (Wiki) Future Research and Development

Accessing SOCR SOCR is divided into 6 major components: Distributions, Experiments, Analyses, Games, Modeler, and Charts. Here, because of time constraint, I will present two sets of applets distributions and experiments.

Distributions FEATURES 45+ Distributions Graphs PDFs CDFs Inverse CDFs Moments

Experiments FEATURES 60+ Experiments Simulations Summary Stats Model vs. Sample

Demonstration of CLT http://www.socr.ucla.edu/

Default Setting for SOCR CLT Applet In this example we can see the binomial distribution (13, 0.4). Using the mouse or the cut-off points left or right) we can compute probabilities of the type P(X>a), P(X>b), or P(a<X<b), or P(X=a). The applet also gives the mean and standard deviation.

A single sample of size n = 16 Normal population In this example we can see the binomial distribution (13, 0.4). Using the mouse or the cut-off points left or right) we can compute probabilities of the type P(X>a), P(X>b), or P(a<X<b), or P(X=a). The applet also gives the mean and standard deviation.

A single sample of size n = 16 Exponential population In this example we can see the binomial distribution (13, 0.4). Using the mouse or the cut-off points left or right) we can compute probabilities of the type P(X>a), P(X>b), or P(a<X<b), or P(X=a). The applet also gives the mean and standard deviation.

100 samples, each of size n = 100 Exponential population In this example we can see the binomial distribution (13, 0.4). Using the mouse or the cut-off points left or right) we can compute probabilities of the type P(X>a), P(X>b), or P(a<X<b), or P(X=a). The applet also gives the mean and standard deviation.

Activities

Future Research and Development In this example we can see the binomial distribution (13, 0.4). Using the mouse or the cut-off points left or right) we can compute probabilities of the type P(X>a), P(X>b), or P(a<X<b), or P(X=a). The applet also gives the mean and standard deviation. SOCR usage Classroom testing for the effectiveness of SOCR (2005-06, 2006-07) New tools under development More SOCR activities for Wiki page SOCR Workshop at UCLA, August 6-8, 2007