# The Eldertons' *Primer of Statistics*

In 1909 W Palin Elderton and Ethel M Elderton published

*Primer of Statistics*. Palin and Ethel Elderton were brother and sister (not husband and wife as one of the reviews suggests). The book was written after Francis Galton had stated in a lecture he gave in 1907 that there was a need for an elementary statistics book. We give below Francis Galton's Preface to the work and extracts from a number of reviews.**1. Note by the Authors.**

We wish to express our thanks to Sir Francis Galton for the original suggestion of this primer and for much kind help and interest throughout its preparation; to Professor Earl Pearson for suggestions and advice on many points; and to Mr C A Sutton for reading the manuscript from the lay point of view.

**2. Galton's Preface.**

In my 'Herbert Spencer' lecture of 1907 before the University of Oxford, I expressed a belief that the elementary ideas on which the modern system of statistics depends, that the quality of the results to which it leads, and that the meaning of the uncouth words used in its description, admitted of much simpler explanation than usual. I sketched out a possible course of lectures to be accompanied with certain simple sortings, with object lessons and with diagrams. Finally, I expressed the hope that some competent teacher would elaborate a course of instruction on these lines. I entertain a strong belief that such a course would be of great service to those who are interested in statistics, but who, from want of mathematical aptitude and special study, are unable to comprehend the results arrived at, even as regards their own subjects. It is, for example, a great hindrance to have no knowledge of what is meant by 'correlation'.

I learnt with much pleasure that two very competent persons were disposed to undertake the task - namely, Mr W Palin Elderton, well known as a highly instructed actuary, and his sister, Miss Ethel M Elderton, who holds the post of Research Scholar in the Eugenics Laboratory of the University of London (now located in University College), and who is a thoroughly experienced worker in the modern methods.

This primer is the result. It goes forth on its important errand of familiarising educated persons with the most recent developments of the new school of statistics, and, I beg to be allowed to add, with my heartiest good wishes for its success.

**3. Introduction.**

If you will go into the garden and pick a number of leaves from a tree, you will find that they are not all of the same size; some leaves, even though they are fully grown, will be much smaller than others, and if you were to measure their lengths, you would find a considerable difference between the longest and shortest specimens in your collection. You would probably obtain similar results in any other class of objects you collected, and if you were asked what was the size of the leaf of a particular tree, or the size of a certain kind of nut or shell, you would have to reply that, as you found all sorts of sizes, you could not give an exact answer. You could explain that these things always varied because of the many causes that affect size; but if you thought the matter over, you would not be long in seeing that such an explanation did not supply a full answer to the question, but merely accentuated your inability to give one. Let us see if we can find some way of working out an answer, and of expressing the results of your measurements in an intelligible form.

**4. Review by: Allyn A Young.**

*Publications of the American Statistical Association*

**12**(92) (1910), 385-386.

The Primer of Statistics is designed to carry out a suggestion of Sir Francis Galton (who contributes a preface to the book) to the effect that the elementary concepts of the modem system of biometric statistics might be explained in a much simpler fashion than has been usual. In this aim the authors have succeeded: the book is, indeed, a veritable primer. Frequency distributions and their important constants, such as the median, quartile, mode, standard deviation, and coefficient of correlation, are explained in a very elementary way and are illustrated by concrete examples of the distribution of cricket scores and of simple biometric data. The discussion does not penetrate into the subject far enough to be of service to one who wishes to know how to handle frequency distributions in actual statistical investigation. It will probably have achieved its purpose if it appreciably enlarges the audience to which an exposition of the results of the use of these methods will be intelligible. The authors tread on dangerous ground (for an elementary treatise) when, like others of their school, they suggest the abandonment of the use of the "probable error of an average" in favour of the "standard deviation of an average." Their statement that the use of the older constant assumes that the frequency distribution dealt with follows the normal curve of error is thoroughly misleading, for it takes no account of the frequently found conditions under which averages of quantities not distributed in accordance with the normal law will themselves follow this law. Moreover, the "probable error" has certain advantages of its own.

**5. Review by: W B B.**

*The Economic Bulletin*

**3**(4) (1910), 423-424.

The Primer of Statistics is one of the most useful books upon the theory of statistics which have appeared in English, for it contains in a few pages and in terms intelligible to a person who is not competent to deal with higher mathematics, the principles which should govern the abstraction of statistical data. The arrangement of the book is extremely clear and logical. The first chapters deal with the mean, median, mode, and frequency distribution. The short chapter devoted to standard deviation could not well be improved. Perhaps the section of most value to the average student is that on correlation. This method is so commonly used by the new school of statistics that a short treatment of this kind is timely. It is unfortunate that this subject was not developed further with more extended reference to the methods ordinarily employed. In the concluding chapter upon probable error the reader is left somewhat in doubt as to the value which should be chosen. In the hands of a competent teacher, this little book should prove of value as a text. In a treatment of such brevity much is of necessity omitted, but reference to the volumes mentioned in the footnotes would enable an ambitious student to supply these deficiencies. The book will repay careful reading by students of economics and sociology who wish to avoid the pitfalls of statistics.

**6. Review by: A D W.**

*Journal of the Royal Statistical Society*

**73**(2) (1910), 170-171.

A primer of statistics discussing in non-technical language the principal terms and ideas of statistical science has long been a desideratum. The present work goes a long way towards satisfying this need. The headings of the six chapters are technical enough, namely: I. Variates and Medians; II. Quartiles and Means; III. Frequency Distributions; IV. Mode, Standard Deviation, Coefficient of Variation; V. Correlation; and VI. Probable Errors; but the authors have succeeded, with the help of a few homely illustrations, in making the meaning of these various terms and much of their significance clear to any careful and intelligent reader. It is made perfectly plain that very diverse groups of facts

may be statistically described by "curves of error," although the authors leave undiscussed the natural question whether and, if so, why such curves can be expected to arise on a priori grounds. Since the book has been written with the purpose, as expressed in the preface by Sir Francis Galton, "of familiarising educated persons with the most recent developments of the new school of statistics," by explaining the technical terms and elementary ideas of that school, it is, perhaps, hardly fair to suggest that the book barely goes far enough in its treatment of the practical side of statistics. For instance, in dealing with correlation, the method "which would be employed in practical work" is not described, but the reader is referred elsewhere for a knowledge of it. The methods actually described in the book, especially the graphic method, while serving the authors' purpose of explaining the idea of correlation, are rather crude, and may yield very inexact results, so that we think reference could have been usefully made to the formula

$r = \Large \frac{\sum xy}{\sigma_1 \sigma_2}\normalsize n$

and its use exemplified without entering into the mathematics of the coefficient. We advance this criticism, however, not to disparage what is actually a useful introduction to statistics, but rather to indicate that there still remains room for an elementary book which shall go farther than the present one without engaging in the mathematical complications of the science.
**7. Review by: Anon.**

*The Mathematical Gazette*

**6**(92) (1911), 101.

To familiarise "educated persons with the most recent developments of the new school of statistics" is the aim of this valuable little primer. Mrs Elderton is a Galton Research Scholar in National Eugenics, Mr Elderton is a Fellow of the Institute of Actuaries, and the primer was issued to the world with the blessing of Sir Francis Galton. The "educated person" will not be led astray if he begins his study of statistics under such guidance. The scope of this handy and useful manual will be gauged from the titles of the chapters: variates and medians; quartiles and medians; frequency distributions; mode-standard deviation-coefficient of variation; correlation of probable errors. The treatment is as simple and clear as it can be made, and while the teacher should be familiar with the subject matter, both as "educated person" and in his professional capacity, the boy will find the study of most of the contents a very agreeable holiday task. Few boys will not revel in Chapter iv., which studies amongst other things the two problems: What was Tunnicliffe's most likely score in 1906? Was he a consistent batsman? Warner's scores are utilised in the same way to exhibit the meaning of the "sort of" average measure of deviation, to which is given the name of standard deviation.

**8. Review by: Anon.**

*Nature*

**82**(426) (1910), 426.

In his Herbert Spencer lecture of ]907, Sir Francis Galton outlined a suggested course of "Object lessons in the Methods of Biometry," adapted to persons with no mathematical knowledge. The course was to consist of five lessons, the first to introduce the learner to the idea of variability and the median, the second to deal with the scheme of distribution (the ogive curve), the third with deviations from the median, the fourth with frequency curves (including the arithmetic mean and the standard deviation ), and the fifth with correlation.

The present little volume owes its genesis to this suggestion of Sir Francis Galton, who contributes a short preface, and it follows very much the lines he laid down, with the addition, however, of a chapter on probable errors. The style is for the most part very simple, and the volume should be of real service to biological students and others who desire to obtain a general idea as to the meaning of the terms used in modern statistical methods. A few statements seem, however, to be open to criticism. The student ought not to conclude that "shells possess a mid-length (or median) which is constant in different samples" when he has only examined two samples. It is hardly correct to state that "when the difference between two means exceeds three times the probable error, then it is considered to be certain that the difference is significant"; it is merely moderately likely. Finally, while it is true that the theory of errors of sampling "depends on the assumption that the things dealt with have been taken at random" (a word which does not appear to be defined), we cannot agree with the unqualified statement that "the collection of statistics in any other way is sheer waste of time," nor that "it is far better ... to take 5000 or 6000 cases at random ... than to take 50,000 which are specially chosen"; the contrary, indeed, may often be the case.

In the first chapter, we also suggest, it would be better to use longer series as illustrations; Figs. 2, 3 and 5 especially, hardly suggest the true form of the "ogive" to anyone who is not prejudiced by a wider experience than the readers of this book are assumed to possess, and scarcely justify the statement made on p. 6 as to the form of the curve. A second edition of this little volume is sure to be called for, as it fills a distinct gap in statistical literature, and the points mentioned might receive consideration.

Last Updated September 2021