Between Certainty and Uncertainty

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This unique short course on statistics offers a captivating introduction for students, engineers, and researchers, featuring historical insights and 80 numerical examples across five units. Chapter 1 covers descriptive statistics, focusing on compressing small samples, basic averages like mean and variance, their properties, and z-scored statistics. Chapter 2 introduces grouped data, discussing Udny Yule’s qualitative and quantitative variables, graphical tools, frequency histograms, and the significance of percentiles. Chapter 3 delves into regression and correlation, exploring geometrical distances, the interpretation of regression lines, and the correlation coefficient, with engaging examples like Hubble's observations. In Chapter 4, the origins of the binomial distribution are traced back to the Middle Ages, including combinatorial rules and Pascal’s Arithmetical Triangle, alongside discussions on Bernoulli and Poisson trials and Jacob Bernoulli’s Weak Law of Large Numbers. Finally, Chapter 5 examines the normal distribution and its connection to binomial heritage, presenting tables of the normal distribution and insights from Abraham de Moivre and the second theorem of de Moivre-Laplace. This course is a comprehensive guide to understanding essential statistical concepts and their applications.