# Laws of Large Numbers

• ### Cartoon: Genie

A cartoon that provides a good way to introduce the Law of Large Numbers using the negative expectation for games of chance at a casino. The cartoon was used in the March 2022 CAUSE cartoon caption contest and the winning caption was written by Rich Einsporn from the University of Akron.  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 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: Law of Large Numbers

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

• ### Quote: Manley on Revealing Secrets

A quote that might be used in discussing the Law of Large Numbers. The quote is by English author and satirist Delarivier Manley (1663 â€“ 1724) from her 1709 book "Secret Memoirs and Manners of Several Persons of Quality of Both Sexes."
• ### **Histogram Explorer

This applet is designed to allow users to explore the relationship between histograms and the most typical summary statistics. The user can choose from several types of histograms (uniform, normal, symmetric, skewed, etc.), or can create their own by manipulating the bars of the histogram. The statistics available for display are mean, median, mode, range, standard deviation, and interquartile range. Also available is a "Practice Guessing" option, in which the values of the statistics are hidden until the user has entered guesses for each value.
• ### Quote: Cooper on The Law of Large Numbers

Oh, well, this would be one of those circumstances that people unfamiliar with the law of large numbers would call a coincidence. is a quote spoken by Sheldon Cooper (2007 - ) a character on the CBS comedy show "The Big Bang Theory" played by Jim Parsons (1973 - ). The quote occurred in Season 1 episode 4 that first aired in October, 2007.
• ### Cartoon: Scatterplot Outlier

A cartoon to teach about outliers in scatterplots. The cartoon is #114 in the "Life in Research" series at www.vadio.com. Free to use with attribution in the classroom or on course websites.
• ### Cartoon: The Graffiti Wall

A cartoon to teach the idea that averages are less variable than individual values. The cartoon is free for use on course websites or in the classroom. Commercial uses must contact the copyright holder - British cartoonist John Landers (cartoons@landers.co.uk) who drew this cartoon based on an idea from Dennis Pearl.
• ### Webinar: Statistics Video Wrappers: Moving It Out of the Classroom with PreLabs

Many introductory Statistics courses consist of two main components: lecture sections and computer laboratory sections. In the computer labs, students often review fundamental course concepts, learn to analyze data using statistical software, and practice applying their knowledge to real world scenarios. Lab time could be better utilized if students arrived with 1) prior exposure to the core statistical ideas, and 2) a basic familiarity with the statistical software package. To achieve these objectives, PreLabs have been integrated into an introductory statistics course. A simple screen capture software (Jing) was used to create videos. The videos and a very short corresponding assignment together form a PreLab and are made available to students to access at appropriate times in the course. Some PreLabs were created to expose the students to statistical software details. Other PreLabs incorporate an available online learning resource or applet which allows students to gain a deeper understanding of a course concept through simulation and visualization. Not all on-line learning resources are ready to use 'as in' in a course. Some may be lacking a preface or description on how they are to be used; others may use slightly different notation or language than your students are accustomed to; a few may even contain an error or item that needs some clarification. One solution to such difficulties was to create a video wrapper so students can see how the applet works while receiving guidance from the instructor. In this webinar we will share the success story of how one introductory Statistics course integrated these video wrappers into the course and the discuss other possible applications.