# Limit Theorems

• ### Quote: Wright on the Law of Averages

While nothing is more uncertain than the duration of a single life, nothing is more certain than the average duration of a thousand lives. A quote of American actuary and abolitionist Elizur Wright (1804 - 1885).
• ### Quote: Mauldin on the Law of Averages

I feel like a fugitive from the law of averages. A quote of soldier and U.S. cartoonist William H. Mauldin (1921 - 2003) from a cartoon caption in the first published collection of his work, "Up Front" (H. Holt and Co., 1945)
• ### Quote: Stamp on Data Quality

The individual source of the statistics may easily be the weakest link. Harold Cox tells a story of his life as a young man in India. He quoted some statistics to a Judge, an Englishman, and a very good fellow. His friend said, Cox, when you are a bit older, you will not quote Indian statistics with that assurance. The Government are very keen on amassing statistics ... they collect them, add them, raise them to the nth power, take the cube root and prepare wonderful diagrams. But what you must never forget is that every one of these figures comes in the first place from the `chowty dar` [village watchman], who just puts down what he damn pleases." Quoted from "Some Economic Factors in Modern Life" (King and Son, 1929; p. 258) by Sir Josiah Charles Stamp (1880 - 1941), British economist, statistician, director of the Bank of England and president of the Royal Statistical Society.
• ### Regression Applet

This applet was designed to illustrate the impact on simple linear regression output caused by adding a new data point. The applet simulates data and provides a graphical display of the data points and fitted regression line as well as the updated regression line after the addition of a data point.
• ### Sampling distribution of the mean

This FLASH based applet illustrates the sampling distribution of the mean. This applet allows the user to pick a population from over 2000 pre-defined populations. The user can then choose size of the random sample to select. The applet can produce random samples in one, 10, 100, or 1000 at a time. The resulting means are illustrated on a histogram. The histogram has an outline of the normal distribution and vertical lines at 1, 2, and 3 standard deviations. The applet can be viewed at the original site or downloaded to the instructors machine.
• ### Song: Statistician

Song incorporates various terms from areas such as experimental design, graphing, and hypothesis testing. May be sung to the tune of "Desperado" (The Eagles). Musical accompaniment realization are by Joshua Lintz and vocals are by Mariana Sandoval from University of Texas at El Paso.

• ### Sampling Distributions of the Sample Mean: A Fathom Project

During this simulation activity, students generate sampling distributions of the sample mean for n = 5 and n = 50 with Fathom 2 and use these distributions to confirm the Central Limit Theorem. Students sample from a large population of randomly selected pennies. Given that the variable of interest is the age of the pennies, which has a geometric distribution, this is a particularly convincing demonstration of the Central Limit Theorem in action. This activity includes detailed instructions on how to use Fathom to generate sampling distributions. The author will provide the Fathom data file upon request.
• ### Spinning Wheel

This activity uses a computer program to explore probability concepts such as sample space, independent events, law of large numbers, and reliability. An outline of the activity and the computer program are provided.
• ### Sampling SIM: Simulation Software

This program allows the student to explore the nature of sampling distributions of sample means and sample proportions. The software provides separate windows for building population distributions, drawing and viewing random samples from the population, exploring the behavior of sampling distributions of sample means, and exploring the behavior of confidence intervals.
• ### Random Babies Applet

This applet simulates randomly assigning newborn babies to families and measures the number of matches, or instances when a baby is assigned to its real family. The applet keeps track of each trial and records the information in a histogram. The idea is to teach theoretical values associated with random sampling. The relation website is a worksheet activity to accompany the applet.