## Statistics: a graphic guide

### By Eileen Magnello and Borin van Loon

Statistics are emotive — to some they are just lies, to others perplexing, some fear their power to reduce us all to a single number, while yet others (politicians and journalists especially) like to endow them with qualities like "damning" or "deathly". So what are (or should it be "is"?) statistics all about? And what do we need to be wary of? This little comic-style book (from the *Introducing* series) provides some friendly answers in 176 pages and a handy A6 format. For those naturally scared of approaching this maths-heavy topic, the book provides an intuitive introduction set in historic and social context. Even for those who are not, it's a handy reference guide to some of the central concepts that is far more entertaining than your usual text book.

The most striking thing about this book are the illustrations by Borin van Loon. The text, written by Eileen Magnello, appears around them, within them, in speech bubbles, or even framing them, so rather than being little asides, the illustrations are absolutely central to the book. They depict a variety of things, from the obvious visual pun (Poisson has the body of a fish) to the downright bizarre. There are plenty of portraits of statistical protagonists in strange juxtaposition with what they were working on, women emerging from fat suits or living in other people's hair, giants, dwarves, cave men and three-armed mathematicians illustrating coordinates axes. This format is slightly confusing at first, but once you get your eye in, it turns what could be a rather dry experience into light reading, with your brain able to rest while you marvel at a picture or laugh at a cartoon.

In terms of content, the greatest asset of the book is the context it provides. I personally am a recent convert to the marvels of statistics. At school and university, stats to me was a set of perplexing mathematical tools to be applied parrot-fashion to parrot problems, mostly to do with testing if a factory produces too many sub-standard nails. What I was lacking was the kind of historical background given in this book, which reveals just how fascinating the topic is. Rooted to a large extent in the social upheaval of the industrial revolution, modern statistics was driven by a desire to understand the masses and by questions that weren't about nails at all. Its results have affected millions — statistical observations led to important 19th century health reforms — and thrown up deeper questions about the meaning of averages and variation. Statistics is also a curiously double-edged beast: designed to analyse information with utmost objectivity, it's at the same time a powerful tool to mislead.

The book starts off by extending a reassuring hand to those who are nervy about statistics. It acknowledges its ambiguous standing, quoting Courtney's (and not Disraeli's!) obligatory "lies, damn lies, and statistics" and a hilarious "cigarettes are the biggest single cause of statistics" by an unknown columnist. But right at the start the book also makes the important point that mathematical statistics is not about averages, but on the contrary about capturing and measuring variation. There is an interesting reference to Darwin's work on natural selection, which represented an ideological shift away from the "idealised mean" bearing the essence of a species, and towards the variation that enabled it to evolve. As the book points out, Darwin was the first to view evolution as a statistical process. This type of philosophical shift, which occurred in the middle of the 19th century, combined with the Victorians' fascination with all things measurable provided the perfect breeding ground for modern statistics, as well as a starting idea of the book.

In what follows we travel back to the beginnings of data collections, meeting the likes of Thomas Cromwell and the astronomer Edmond Halley, before delving into Victorian statistics, including Florence Nightingale's important statistical observations in military hospitals. The mathematical concepts begin in earnest with a section on probability theory, which then leads to all the concepts that should be part of a beginner's guide to statistics: probability distributions, the central limit theorem, different types of averages and how they can mislead, measures of variation and correlation, regression to the mean and how to fit models. The book ends with a pointer to inferential statistics, which has given us vital applications like opinion polls and medical statistics.

The context provided throughout the book does wonders for mathematical comprehension. Once you understand the problems that faced the statistical protagonists, it's far easier to make sense of the mathematical solutions they came up with. And the resulting mathematical concepts are defined rigorously alongside the drawings and historical anecdotes. This approach of explaining the real meaning, in plain English, of statistical concepts makes these definitions much easier to digest. So if you're nurturing an amateur interest in statistics, then this book offers an entertaining dip-in-and-out way of getting your head around some of the central concepts. For the more serious student, it makes a great companion to your old-school text book.

*You can also read Eileen Magnello's Plus article Florence Nightingale: The compassionate statistician.*

**Book details:***Statistics: A graphic guide*- Eileen Magnello and Borin van Loon
- paperback — 176 pages (2009)
- Icon Books Ltd
- ISBN: 978-1848310568

### About the author

Marianne Freiberger is co-editor of *Plus*.

## Statistics: a graphic guide

Unfortunately the explanation of Central limit theorem in this nice book is entirely false!

Who will repaire it and when ?

dr. J.Hendl, Charles University, Prague

:-(

## Understanding statistics -- or not!

Not everything in this book is bad: the historical information is very interesting. (The author has a PhD in the history of science.)

Unfortunately, however, the book is riddled with blunders and misconceptions, obfuscations and inaccuracies.

Consider just one topic: the standard deviation -- pretty important when it comes to understanding statistics.

We are told that the standard deviation 'indicates how widely or closely spread the values are in a set of a data' (fine so far, apart from the typo of an extra 'a'), and then that it 'shows how far each of these individual values deviate from the average'. No: as a single summary figure, the standard deviation cannot possibly give information on 'each of these individual values'. (That is not its purpose, of course; indeed it almost the exact opposite of its purpose.)

The accompanying graphic carries the information that the 'standard deviation ... corresponds to the moment of inertia ... of dynamics'. No: it corresponds to the radius of gyration. And we are told that the moment of inertia is 'a geometrical property of a beam, and a measure of the beam's ability to resist buckling or bending'. Oh dear! Clearly the author's grasp of mechanics is no better than her grasp of statistics.

The formula for the standard deviation is then given -- but it is typeset incorrectly!

Next, the standard deviation for a set of data (with mean 8) is calculated (correctly!) as 2.82. The accompanying comment is 'This means that the average amount of deviation in this set of data is 2.82 units away from the mean value of 8 and that, therefore, there is a small amount of variation in this sample'. There appears to be no explanation of the criterion by which the variation is deemed large or small. Certainly it is not a criterion known to this statistician.

Finally, we have 'Although the standard deviation indicates to what extent the whole group deviates from the mean, it does not show how variable a particular group is.' I have read that over and over again and I am at a loss to know what it is trying to say.

I wish I could say that the other statistical concepts in the book fared better than the standard deviation -- but they don't. I can't resist mentioning the coefficient of variation which is said to be useful in comparing the variability of temperatures in two cities, one set of measurements being in in degrees Celsius and the other in Fahrenheit. This, of course, is a perfect example of when it would *not* be appropriate to use the coefficient of variation -- because the mean could be zero and the coefficient of variation would then be infinite.

If you understand anything about statistics this book will infuriate you; if you don't understand much about statistics the book will hinder not help.

Avoid!