Limit Theorems

  • 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.  

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  • 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).

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  • 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.

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  • 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.

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  • A song that can be used in discussing the convergence of the sample proportion to the true probability as the number of independent trials grows larger. 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 1967 song “Bare Necessities,” written by Terry Gilkyson for the animated Disney film The Jungle Book. Also, an accompanying video may be found at https://www.youtube.com/watch?v=mBWKGEpQ2tk

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  • 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

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  • A quote that might be used in discussing the Law of Large Numbers. The quote is by English author and satirist Delarivier Manley (1663 – 1724) from her 1709 book "Secret Memoirs and Manners of Several Persons of Quality of Both Sexes."
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  • A poem consisting of two quasi Haikus that can used in discussing the Cramer-Rao lower bound on the variance of a normally distributed statistic. The poem was written by Ming-Lun Ho of Chabot College and was given a third place award in the 2015 A-mu-sing contest.
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  • 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.
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  • A poem for teaching about the Cramer-Rao lower bound on variance of estimators. The poem was written by Ming-Lun Ho, Chabot College. It won third place in the non-song category of the 2015 A-Mu-Sing competition.
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