Itâ€™s a girl! Random numbers, simulations, and the law of large numbers. (English)

Math. Teach. Middle Sch. 20, No. 9, 561-563 (2015).

Summary: Modeling using mathematics and making inferences about mathematical situations are becoming more prevalent in most fields of study. Descriptive statistics cannot be used to generalize about a population or make predictions of what can occur. Instead, inference must be used. Simulation and sampling are essential in building a foundation for statistical inference. This article describes an activity that addresses the National Council of Teachers of Mathematics (NCTM) Standards regarding students using proportionality and having a basic understanding of probability to make and test conjectures about the results of experiments and simulations. This activity also addresses the Common Core State Standards for School Mathematics (CCSSM) directive about statistics, which states that students need to understand that statistics can be used to gain information about a population by examining a sample of the population, and that generalizations about a population from a sample are valid only if the sample is representative of that population. Students should also understand that random sampling tends to produce representative samples and support valid inferences. The activity in this article addresses how to estimate a theoretical probability from sample statistics when compiling the data of an entire class. Students will learn how to sample and use different tools to simulate an outcome. As the number of trials increases, the law of large numbers states that the experimental probability will approach the theoretical value. (ERIC)