Descriptive statistics One and two-dimensional variable

This book is a corrected and expanded version of the book [7] published in 2006 on one- and two-dimensional descriptive statistics. It is obviously not the same version, except perhaps for a slight similarity in the arrangement of the various concepts underlying this part of mathematical statistics in general. Descriptive statistics is taught in high schools and in the first cycles of higher education. How can we provide interesting and new information for readers who have, for the most part, studied this subject? This is not an easy problem to solve, given that there are a wide range of books, both in print and electronic formats, which cover this subject. The main objective, in my opinion, is to start with a statistical study that consists of collecting numerical observations, formulating hypotheses, and validating them in order to arrive at recommendations and enable the most beneficial decisions to be made. This work must be part of this perspective and it is a considerable contribution which allows users of statistics to study and analyze their data in order to draw an appropriate interpretation. This book covers all aspects of this part of mathematical statistics, known as one- and two-dimensional descriptive statistics. This is a topic that encompasses many mathematical techniques. Some existing works supplement each method stated with a program in R or other software for the necessary calculations. This is of course important and adapts to the current context where computing has become a tool within everyone's reach. But what more can an author, however experienced, do? We have consulted many books that deal with this very important topic because it opens many perspectives regarding its application in multiple areas of social and economic life. The observation is that very few books talk about how to interpret the output results. How to make the numbers speak and how not to make them speak in doubt and in non-doubt? Aristotle said in his time that "the ignorant confirms, the learned doubts and the wise reflects." These words remain eternal and adapt perfectly to the language of statistics. We have to know the method in all its aspects, have common sense and therefore wisdom to draw useful and profitable conclusions. We have tried to tackle this in order to say what must be said and avoid saying what must not be said. This book is also organized into eight loosely related chapters that bring together everything that can be said about one- and two-dimensional statistical descriptions. It also discusses the limitations and extensions of the various methods presented. The exercise sections are divided into two subsets: a set of exercises with standard answers and a set where the exercises are presented without answers. We offer statistics to those who want to exercise their minds and also to those, many who want to satisfy their passion for mathematics and dare to make numbers speak.