# Limit Theorems

• ### Song: Means Will Follow You

A song describing how sample means will follow the normal curve regardless of how skewed the population histogram is, provided n is very large.  The lyrics were written by Dennis Pearl and Peter Sprangers, both then at The Ohio State University.  The audio recording was produced by The University of Texas at El Paso student Nicolas Acedo who also performed the vocals

• ### Cartoon: Ice Cream Sales

A cartoon using a classic example for teaching the idea that correlation does not imply causation. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl and Deb Rumsey (The Ohio State University). Free to use in the classroom and on course web sites.
• ### Cartoon: Two Casinos

A cartoon to teach about the law of large numbers and the expected value under the assumption that future events are unknown to the betting strategy. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl (The Ohio State University). Free to use in the classroom and on course web sites.
• ### Standard Errors and The Central Limit Theorm

This lesson introduces the Central Limit Theorem and discusses it in terms of the normal distribution, binomial distribution, and Poisson distribution.
• ### Graphical Table of Normal Distribution

This applet relates the pdf of the Normal distribution to the cdf of the Normal distribution. The graph of the cdf is shown above with the pdf shown below. Click "Move" and the scroll bar will advance across the graph highlighting the area under the pdf in red. The z-score is shown as well as the probability less than z (F(z)) and the probability greater than z (1-F(z)).
• ### How Statistical Educators Can Attract Students to the Discipline of Statistics

This website is a resource of teaching methods and approaches that instructors at all levels of statistics education can use to generate student interest in pursuing more study or a career in the field of statistics.
• ### Sampling Distribution Simulation

This applet demonstrates the Central Limit Theorem. First, select a distribution (Normal, Uniform, Skewed, Custom) and add or delete data points by clicking on the graph. Then, sample from the parent population and the distribution of the sample mean is shown. Users can also choose to see the distribution of the median, standard deviation, variance, and range.
• ### Analysis Tool: Normal Distribution Table

This page provides a z-table with alpha levels from .00 to .09.

• ### Wilcoxon-Mann-Whitney U Test JAVA Calculator

This calculator determines the level of significance for the Wilcoxon-Mann-Whitney U-statistic. Users can enter N1, N2, and U or simply enter the raw data.