The sixth edition of Meaningful Statistics introduces students to foundational concepts and demonstrates how statistics are an integral aspect of their everyday lives-from baseball batting averages to reports on the median cost of buying a home to the projected outcomes of an upcoming election. Each chapter begins with a question and scenario that is then explored through statistical concepts, demonstrating to students how research and statistics can help us to answer questions and solve problems. The opening chapter focuses on the process of collecting data and uses this information to explore whether multivitamins are a waste of money. Additional chapters explore linear regression and whether junk food is harmful to a child's IQ; normal distribution and the issue of a tie for Olympic downhill gold; confidence intervals and a simulation of the NBA draft lottery; and more. Students learn about descriptive measures for populations and samples; probability and random variables; and sampling distributions, with each concept corresponding to real-world examples. Closing chapters cover the testing of hypotheses, tests using the chi-square distribution; and inferences with two or more populations. For the sixth edition, exercises and examples have been updated throughout. Designed to bring key concepts to life, Meaningful Statistics is an ideal resource for courses in mathematics and statistics.

This volume presents lectures given at the Wisła 20-21 Winter School and Workshop: Groups, Invariants, Integrals, and Mathematical Physics, organized by the Baltic Institute of Mathematics. The lectures were dedicated to differential invariants – with a focus on Lie groups, pseudogroups, and their orbit spaces – and Poisson structures in algebra and geometry and are included here as lecture notes comprising the first two chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and category theory. Specific topics covered include: The multisymplectic and variational nature of Monge-Ampère equations in dimension four Integrability of fifth-order equations admitting a Lie symmetry algebra Applications of the van Kampen theorem for groupoids to computation of homotopy types of striped surfaces A geometric framework to compare classical systems of PDEs in the category of smooth manifolds Groups, Invariants, Integrals, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry and category theory is assumed.