1. 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
MERLOT International Conference
New Orleans, Louisiana
August 9, 2007

2. 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

3. 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.

4. Distributions FEATURES 45+ Distributions Graphs PDFs CDFs Inverse CDFs
Moments

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

6. Demonstration of CLT

7. 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.

8. 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.

9. 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.

10. 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.

11. Activities

12. 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 ( , )
New tools under development
More SOCR activities for Wiki page
SOCR Workshop at UCLA, August 6-8, 2007