Between certainty and uncertainty. Statistics and probability in five units with notes on historical origins and illustrative numerical examples (Q655141)

As mentioned on the cover page, this Volume 31 from the Intelligent Systems Reference Library describes certain aspects of statistics and probability in five chapters (units) with notes on historical origins and illustrative numerical examples. It consists of two parts (called ``Book one'' and ``Book two''), each divided into five chapters (units). The first chapter of Book one, titled ``Descriptive statistics'', starts with a dialogue between `the student' and `the author', following the Polish writer Gombrowicz. `The author' explains why he has chosen to develop ``a special branch of statistics dealing with logistics as its main field of applications''. This chapter introduces the conventional measures of location and dispersion and ends with the concept of \(z\)-scores. In Chapter 2, these ideas are extended to calculations from grouped data including percentiles. Descriptive statistics of two dimensions, namely regression and correlation, is the theme of Chapter 3. The content of Chapter 4 is about the interesting history and the origins of the binomial distribution, and the final Chapter 5 describes the normal approximation to the binomial distribution and explains the properties of the distribution of sample means. Book two, titled ``Exercises'', illustrates the above concepts chapter-wise using real data of around 80 examples. It is indeed a difficult task to trace the origins and the history of elementary statistical concepts as chosen in this volume in 160 pages, and the author has given a nice account especially relating to certain Polish statisticians. While discussing Neyman, it may be relevant to point out that Neyman's contribution in the Journal of Royal Statistical Society in 1934, referring to optimum allocation of sample size in stratified sampling, relates to an earlier work of 1923 by Tschuprov published in Metron. Also, in the context of the contributions of European statisticians, Quetelet's work could have been quoted in this volume. The author describes (p. 31) how Gosset's (Student's) work was not acknowledged by Karl Pearson, but Fisher called the approach a ``logical revolution''. It is perhaps not out of place to mention that Karl Pearson did not accept Mahalanobis's work on D2 statistic, while it was again Fisher who appreciated and termed it ``Mahalanobis distance''. There is a passing reference to the Indian mathematician Bhaskara (p. 89) from the 12th century who provided a well-known algorithm for the Pascal triangle among many other contributions. It is not clear why the calculations in the volume are given to a large number of decimal places, even though the author says (p. 73) that for practical purposes (calculations) it can be rounded to four digits. Furthermore, today's computer-savvy student may not appreciate the calculation of correlation coefficients or regression lines showing the cross checks and all other details. At the end, the volume has about 100 references and a 4-page index. For the researcher interested in historical aspects, this volume is a welcome addition. Probably, future editions may consider adding more chapters and leaving the solution of exercises to the user (student).