This activity helps students develop a better understanding and stronger reasoning skills about the Central Limit Theorem and normal distributions.

Key words: Sample, Normal Distribution, Model, Distribution, Variability, Central Limit Theorem (CLT)

Your basketball team is down by one point! Your teammate, who makes free throws about three-fourths of the time, is at the free-throw line. She gets a second shot if she makes the first one. Each free throw she makes is worth one point. If there is no time left, what are the chances you win the game without overtime?

Advertisers constantly thrust quantitative information in our face. Product claims, store enticements, health benefits, and scores of other contexts use short quantitative arguments to catch a reader's eye (and possibly money). This example shows how one can use these ads to bring added content to a quantitative reasoning course.

This activity has students use Fathom to test the correlation between attendance and ballpark capacity of major league baseball teams by taking a sample of actual data and scrambling one of the variables to see how the correlation behaves when the variables are not related. After displaying the distribution of correlations for many simulated samples, students find an approximate p-value based on the number of simulations that exceed the actual correlation.

In this video segment from Cyberchase, the CyberSquad determines the fairness of a game in which there are three shapes distributed equally on nine squares.

Dawson (1995) presented a data set giving a population at risk and fatalities for an “unusual episode” (the sinking of the ocean liner Titanic) and discussed the use of the data set in a first statistics course as an elementary exercise in statistical thinking, the goal being to deduce the origin of the data. Simonoff (1997) discussed the use of this data set in a second statistics course to illustrate logistic regression. Moore (2000) used an abbreviated form of the data set in a chapter exercise on the chi-square test. This article describes an activity that illustrates contingency table (two-way table) analysis. Students use contingency tables to analyze the “unusual episode” data (from Dawson 1995) and attempt to use their analysis to deduce the origin of the data. The activity is appropriate for use in an introductory college statistics course or in a high school AP statistics course.

Students explore the definition and interpretations of the probability of an event by investigating the long run proportion of times a sum of 8 is obtained when two balanced dice are rolled repeatedly. Making use of hand calculations, computer simulations, and descriptive techniques, students encounter the laws of large numbers in a familiar setting. By working through the exercises, students will gain a deeper understanding of the qualitative and quantitative relationships between theoretical probability and long run relative frequency. Particularly, students investigate the proximity of the relative frequency of an event to its probability and conclude, from data, that the dispersion of the relative frequency diminishes on the order .

This activity provides students with 24 histograms representing distributions with differing shapes and characteristics. By sorting the histograms into piles that seem to go together, and by describing those piles, students develop awareness of the different versions of particular shapes (e.g., different types of skewed distributions, or different types of normal distributions), that not all histograms are easy to classify, that there is a difference between models (normal, uniform) and characteristics (skewness, symmetry, etc.).

This activity leads students to appreciate the usefulness of simulations for approximating probabilities. It also provides them with experience calculating probabilities based on geometric arguments and using the bivariate normal distribution. We have used it in courses in probability and mathematical statistics, as well as in an introductory statistics course at the post-calculus level.

In these activities designed to introduce sampling distributions and the Central Limit Theorem, students generate several small samples and note patterns in the distributions of the means and proportions that they themselves calculate from these samples.

An important objective in hiring is to ensure diversity in the workforce. The race or gender of individuals hired by an organization should reflect the race or gender of the applicant pool. If certain groups are under-represented or over-represented among the employees, then there may be a case for discrimination in hiring. On the other hand, there may be a number of random factors unrelated to discrimination, such as the timing of the interview or competition from other employers, that might cause one group to be over-represented or under-represented. In this exercise, we ask students to investigate the role of randomness in hiring, and to consider how this might be used to help substantiate or refute charges of discrimination.

This is a new approach to an introductory statistical inference textbook, motivated by probability theory as logic. It is targeted to the typical Statistics 101 college student, and covers the topics typically covered in the first semester of such a course. It is freely available under the Creative Commons License, and includes a software library in Python for making some of the calculations and visualizations easier.

This course offers an introduction to probability, statistical mechanics, and thermodynamics. Numerous examples are used to illustrate a wide variety of physical phenomena such as magnetism, polyatomic gases, thermal radiation, electrons in solids, and noise in electronic devices.
This course is an elective subject in MIT’s undergraduate Energy Studies Minor. This Institute-wide program complements the deep expertise obtained in any major with a broad understanding of the interlinked realms of science, technology, and social sciences as they relate to energy and associated environmental challenges.

This course is an introduction to statistical data analysis. Topics are chosen from applied probability, sampling, estimation, hypothesis testing, linear regression, analysis of variance, categorical data analysis, and nonparametric statistics.

This resource is a lesson gudie for an approach to probability that is collaborative among students and designed to have students experience probability from their own unique perspectives. Some of the goals of the work are to:understand the different approaches in probabilitydeepen intuitive experience of probability by facing probabilistic misconceptionsconduct probability experimentsBuilt in as a goal is the soft skill of conducting research for refereed articles, going beyond internet searches and subsequent page hits in terms of curating resources that can lead to success in a probability class.

This course is an introduction to probability and statistics. Students will engage in elementary principles and applications of descriptive statistics, counting principles, elementary probability principles, probability distributions, estimation parameters, hypothesis testing, linear regression and correlation, and ANOVA. Students will utilize the application of technology for various statistical analyses.This assignment asks students to incorporate their identity, skill development, intellect, and critically based on the work of Cultivating Giunus by Dr. Gholdy Muhhamad. Students are asked to analyze the work they have produced throughout the semester and select two works per each student's learning outcome. 

This 10-minute video lesson looks at probability density functions for continuous random variables. [Statistics playlist: Lesson 18 of 85]

This site teaches High Schoolers how to use probability to make decisions through a series of 158 questions and interactive activities aligned to 6 Common Core mathematics skills.

Students will explore the overarching question, is the internet trustworthy?, while expanding their knowledge of statistics and comparing data sets.  They will compare two data sets as well as determine the accuracy or bias of data representations shown on the internet. Students will then have the opportunity to apply their knowledge while creating their own visual representations for data they personally collected regarding the trustworthiness of the internet.  The module concludes with a peer showcase and the post-assessment.

A resource for learning about probability and statistics. The text is motivated by real data and is integrated with interactive features such as applets, videos, and example prompts.