Playfair, William

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This article William Playfair was adapted from an original article by Howard Wainer, which appeared in StatProb: The Encyclopedia Sponsored by Statistics and Probability Societies. The original article ([ StatProb Source], Local Files: pdf | tex) is copyrighted by the author(s), the article has been donated to Encyclopedia of Mathematics, and its further issues are under Creative Commons Attribution Share-Alike License'. All pages from StatProb are contained in the Category StatProb.


b. 22 September 1759 - d. 11 February 1823

Summary. William Playfair, engineer, political economist and scoundrel, was the most important developer of statistical graphics. In the two centuries since, there has been no appreciable improvement on his basic designs.

William Playfair was born at Liff in Scotland during the Enlightenment - a Golden Age in the arts, sciences, industry and commerce. He died in London, in 1823, after an eventful life, though unmarked at the time by any apparently significant or memorable contribution. He made little impression in his native land, and his impact was only slightly greater in England and France. Yet he is responsible for inventions familiar and useful to us all: he was the first to devise and publish all of the common statistical graphs - the pie chart, the bar chart, and the statistical line graph. He invented a universal language useful to science and commerce alike and though his contemporaries failed to grasp the significance, Playfair had no doubt that he had forever changed the way we would look at data. Over a span of thirty six years he published many books and pamphlets containing statistical charts and though this work was received with indifference, even hostility, he never faltered in his conviction that he had found the best way to display empirical data. However, it took almost a century after his death before his invention was fully accepted.

Despite the importance of Playfair's innovations, his name is largely unknown, even to professional statisticians, and those who have heard of him know little of his life. One might expect a life of the inventor of statistical graphs to make dull reading, but Playfair pursued a variety of careers with such passion, ambition, industry, and optimism that even without his great inventions, he would be judged a colorful figure. He was, in turn, millwright, engineer, draftsman, accountant, inventor, silversmith, merchant, investment broker, economist, statistician, pamphleteer, translator, publicist, land speculator, convict, banker, ardent royalist, journalist, editor, and blackmailer. His business activities were sometimes questionable, if not downright illegal, and it may fairly be said that he was something of a rogue and scoundrel (Spence & Wainer (1998)).

A touch of the scoundrel, or at least of the iconoclast, was an important component in the character of anyone who was to develop statistical graphics. The Cartesian tradition of graphical representation of mathematical functions worked against the use of graphs to depict empirical regularities. The switch to the view that a graph can help us formulate an understanding of nature by plotting data and looking for patterns required, in Thomas Kuhn's terms, a shift in paradigm. A person that might effect such a change would not only require the appropriate intellectual and technical background, but would also have to disregard the standards of an academic scientific community that was firmly opposed to illustration in serious writing. In all aspects Playfair fit the bill.

William Playfair was the fourth son of the Reverend James Playfair of the parish of Liff & Benvie near the City of Dundee, Scotland. His father died in 1772 leaving the eldest brother John to care for the family. John was subsequently to become one of Britain's foremost mathematicians and scientists as Professor of Natural Philosophy, Mathematics, and Geology at Edinburgh University. After an apprenticeship at the Houston Mill with Andrew Meikle, the inventor of the threshing machine, William became draftsman and personal assistant to the great James Watt at the steam engine manufactory of Boulton & Watt at Birmingham in 1777. Thus his scientific and engineering training was at the hands of the leading figures of the Enlightenment and Industrial Revolution. On leaving Boulton & Watt in 1782, Playfair set up a silversmithing business and shop in London, but the venture soon failed. Seeking his fortune and hoping to apply his engineering skills to better effect in a developing French economy, Playfair moved to Paris in 1787. He was involved in more than just business in a Paris that was about to undergo revolutionary change. Playfair was one of the approximately twelve hundred inhabitants of the St. Antoine quarter who formed themselves into a militia and assisted in the storming and capture of the Bastille.[1]

In February of 1791 he rescued his friend, the well-known ex-judge, Duval d'Epremesnil from the mob in the Palais Royal Gardens; see Spence & Wainer (1998) for a fuller description of this adventure. He was also a principal in the Scioto debacle - a failed scheme projected to settle migrants between the Ohio and Scioto rivers - about which was said, "some hundreds of unfortunate families were lured to destruction by the picture of a salubrious climate and fertile soil." [2]

Whether on account of alleged mismanagement and embezzlement, or, as Playfair contends, because of his plain speaking against the revolutionaries, Playfair left Paris for Frankfurt in something of a hurry shortly after this adventure.

In 1793, while in Frankfurt, he heard a description of the semaphore telegraph from a French emigre. The following day he built a model of the apparatus and sent it to the Duke of York. He thereafter claimed to have introduced the semaphore into England. although it seems that his major contribution was the introduction of a new alphabet for the device[3]

When he returned to London Playfair opened a "security bank", intended to ease the granting of small loans by subdividing large securities, but this soon collapsed after a conflict with the Bank of England. From the mid-1790s onward he made his living principally as a writer and pamphleteer. Although initially positive, he argued vehemently against the excesses of the French Revolution and wrote frequently on the topic of British policy towards France. He claimed credit for warning of Napoleon's escape from Elba - a warning which the British government ignored. His illustrated British Family Antiquity was a massive nine volume undertaking in which he catalogued the peerage and baronetage of the United Kingdom - a work principally designed to raise money by subscription. He dabbled in journalism, editing more than one periodical, the best known of which may be the Tomahawk. After the restoration of the Bourbons he returned to Paris as editor of the periodical Galignani's Messenger, but in 1818 his comments on a duel between Colonel Duffay and Comte de St. Morys were held to be libelous by the widow and daughter of the latter and led to prosecution. Playfair was sentenced to three months imprisonment, three hundred francs fine, and one thousand francs damages. To avoid incarceration he left France and spent his few remaining years in London writing pamphlets and doing translations. The final two years saw a renewed interest in economics and his final publications include several charts, including one or two rather fine examples that combined the line graph, bar chart, and chronological diagram in a single chart. His interest in agricultural matters was the stimulus for his last two works which examined the difficulties experienced by English farmers in the early nineteenth century.

A common theme throughout Playfair's life was his practical inventiveness. He had a first class knowledge of engineering practice based largely on his experience in Matthew Boulton's manufactory - the world's first modern factory. He took out several patents, mostly involving machines for metal working, including a patent for the first mass-produced silver-plated spoon, but he also proposed innovations such as modifications to the bows of ships to make them faster and improvements to agricultural implements. When he was confronted by a problem he would invariably offer a practical solution - this would often involve the application or adaptation of what he already knew to work well in other situations. Of equal importance was his insistence in recording his proposal. For example, about his arrival in Germany in 1793 he wrote (Spence (1996)),

"When I was in Germany I was surprised that in a country where the milk is excellent the butter was little better than common grease without anything either of the colour or taste that good butter possesses. But one day in changing horses where the post master spoke a little French and had a farm I asked to see the dairy when I found that the milk was kept in deep narrow jars about three feet deep and eight or nine inches wide. The cream that rose to the top was about three inches in depth before it was taken off and though not quite rancid had a disagreeable smell. I advised him to get wide shallow vessels and keep them very clean but he smiled as if I knew nothing of the business. I asked him if the Dutch butter was not better than theirs. He owned it was. I apprised him that the Dutch milk was not so good as the German and that the excellence of the Dutch butter proceeded from the better mode of keeping the milk. He did not attempt to answer my reasoning but gave his head a significant shake and no doubt unless the French soldiers carried them into a better method in Germany they still persist in the same."

In his political and economic writings he often used numerical examples and calculations to make a point, frequently demonstrating the impossibility or absurdity of a commonly held opinion by such calculation. He found that making sense of empirical information was aided enormously by the use of statistical graphics and he believed passionately that graphs, not tables, were the best route to communication and understanding. He used, refined, and adapted those graphical forms that were known to him from mathematics and the natural sciences and invented others. He was the first to use line graphs to portray economic data, including the use of area to depict surplus and deficit; he adapted Priestley's chronological charts to produce the first statistical graph that did not incorporate time as a variable - the bar chart. He created the pie chart and circle diagram seemingly with no intellectual precursors. He was the first to use hachure, shading, and color, thus incorporating elements of classification into the quantitative depiction. The quality and detail of his work was such that in the two centuries since there has been no appreciable improvement of his basic designs. His contributions to the development and demonstrations of the use of statistical graphics in several publications between 1786 and 1822 remain his life's principal accomplishment.

In 1786 he published his Commercial and Political Atlas which contained 44 line graphs and a solitary bar chart (but no maps). This was the first description of his graphical inventions and is the first major work of any kind to contain statistical graphs. It met with limited initial success in England, but fared rather differently in France. Playfair reports[4]

"When I went to France in 1787, I found several copies there, and amongst others, one which had been sent by an English nobleman to the Monsieur de Vergennes, which copy he presented to the king, who being well acquainted with the study of geography, understood it readily, and expressed great satisfaction. This circumstance was of service to me, when I afterwards solicited an exclusive privilege for a certain manufactory, which I obtained. The work was translated into French, and the Academy of Sciences, testified its approbation of this application of geometry to accounts, and gave me a general invitation to attend its meetings in the Louvre; and at the same time did me the honour of seating me by the president during that sitting."

In his unpublished memoirs written shortly before his death (Spence (1996)), Playfair adds, "As his majesty made Geography a study, he at once understood the charts and was highly pleased. He said they spoke all languages and were very clear and easily understood." The extraordinary growth in the use and popularity of statistical graphics in the two centuries since their introduction suggests that Louis XVI 's judgment, in this area at least, was quite correct.


[1] Playfair, W. (1796). For the Use of the Enemies of England: A Real Statement of the Finances and Resources of Great Britain. Stockdale, London.
[2] Playfair, W. (1798). Lineal Arithmetic. A. Paris, London.
[3] Playfair, W. (1786). The Commercial and Political Atlas., (1st ed.) Printed for J. Debrett, London. (3rd ed., 1801) Printed for J. Wallis, London.
[4] Playfair, W. (1809-11). British Family Antiquity. T. Reynolds and H. Grace, London.
[5] Spence, I. (1996). Edited transcription of W. Playfair (1822-23), unpublished MS held by John Lawrence Playfair, Toronto, Canada.
[6] Spence, I. and Wainer, H. (1998). William Playfair: a daring worthless rogue. Chance, 10, 31-34.

  1. Lecocq, Prise de la Bastille
  2. From Gouverneur Morris, Diary.
  3. Credit for both its invention and adoption in the United Kingdom is usually given to Richard Lovell Edgeworth; as nearly as we could determine, this attribution of credit is correct.
  4. This note appears on page iv of the pamphlet Playfair (1796); it was repeated verbatim on page 6 of the introduction to Playfair (1798), and again on page ix in the Introduction to the Third Edition of his 1786 book. He was obviously very fond of the royal treatment he received in France.

Reprinted with permission from Christopher Charles Heyde and Eugene William Seneta (Editors), Statisticians of the Centuries, Springer-Verlag Inc., New York, USA.

How to Cite This Entry:
Playfair, William. Encyclopedia of Mathematics. URL:,_William&oldid=39248