# Central Limit Theorem

• ### Cartoon: Oasis

A cartoon that can be used to discuss the appropriateness of the normal errors assumption in a variety of settings. The cartoon was used in the May 2021 CAUSE cartoon caption contest and the winning caption was written by Dashiell Young-Saver from the Knowledge Is Power Program Public Schools. The cartoon was drawn by British cartoonist John Landers (www.landers.co.uk) based on an idea by Dennis Pearl from Penn State University.

• ### Statistics: Basic Concepts for Astronomers

This presentation was given by Aneta Siemiginowska at the 4th International X-ray Astronomy School (2005), held at the Harvard-Smithsonian Center for Astrophysics in Cambridge, MA.

• ### Song: Central Limit Theorem

A song for use in helping students to recognize when the Central Limit Theorem applies.  Music & Lyrics ©2016 by Greg Crowther from Everett Community College. This song is part of an NSF-funded library of interactive songs that involved students creating responses to prompts that are then included in the lyrics (see www.causeweb.org/smilesfor the interactive version of the song, a short reading covering the topic, and an assessment item).

• ### STatistics Education Web (STEW)

Statistics and probability concepts are included in K–12 curriculum standards—particularly the Common Core State Standards—and on state and national exams. STEW provides free peer-reviewed teaching materials in a standard format for K–12 math and science teachers who teach statistics concepts in their classrooms.

STEW lesson plans identify both the statistical concepts being developed and the age range appropriate for their use. The statistical concepts follow the recommendations of the Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K-12 Curriculum Framework, Common Core State Standards for Mathematics, and NCTM Principles and Standards for School Mathematics. The lessons are organized around the statistical problemsolving process in the GAISE guidelines: formulate a statistical question, design and implement a plan to collect data, analyze the data by measures and graphs, and interpret the data in the context of the original question. Teachers can navigate the STEW lessons by grade level and statistical topic.

• ### Analysis Tool(s): JSE Archive of Interactive Computing (includes JAVA Applets)

The Journal of Statistics Education provides a collection of Java applets and excel spreadsheets (and the articles associated with them) from as early as 1998 on this webpage.

• ### Song: Central Limit Theorem

A song that may be used in discussing the central limit theorem for the sampling distribution of means.  The lyrics were written by Mary McLellan from Aledo High School in Aledo, Texas as one of several dozen songs created for her AP statistics course. The song may be sung to the tune of the classic Christmas song "Jingle Bell Rock" written by Joseph Beal and James Boothe in 1942.  Also, an accompanying video may be found at https://www.youtube.com/watch?v=Mjy0AbJ5rJw

• ### Video: 500 Trials

A video to teach about the central limit theorem and various issues in one-sample hypothesis testing. The lyrics and video were created by Scott Crawford from the University of Wyoming. The music is from the 1988 song "I'm Gonna Be (500 miles)" by the Scottish band The Proclaimers. The video took second place in the video category of the 2013 CAUSE A-Mu-sing competition. Free for non-profit use in classroom and course website applications.
• ### Poem: The Normal Law

The Normal Law is a poem whose words form the shape of the normal density. It was written by Australian-American chemist and statistician William John ("Jack") Youden (1900 - 1971). The poem was published in "The American Statistician" page 11 in v. 4 number 2 (1950).

• ### *Using an Applet to Demonstrate a Sampling Distribution

This in-class demonstration combines real world data collection with the use of the applet to enhance the understanding of sampling distribution. Students will work in groups to determine the average date of their 30 coins. In turn, they will report their mean to the instructor, who will record these. The instructor can then create a histogram based on their sample means and explain that they have created a sampling distribution. Afterwards, the applet can be used to demonstrate properties of the sampling distribution. The idea here is that students will remember what they physically did to create the histogram and, therefore, have a better understanding of sampling distributions.
• ### Quote: Peter on Measurement

If you can't measure it, I'm not interested. A quote by Canadian educator and management theorist Laurence Johnston Peter (1919 - 1990) from "Peter's People" in "Human Behavior" (August, 1976; page 9). The quote also appears in "Statistically Speaking: A dictionary of quotations" compiled by Carl Gaither and Alma Cavazos-Gaither.