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Every bar graph in your maths book and every chart in a news report owes something to William Playfair, a Scottish writer who in 1786 decided that figures about trade and debt should be drawn rather than listed. This post explains what Playfair invented, what he said a chart was for, how to draw a fair bar chart in a worked example, and the mistakes that make charts mislead.
Who was William Playfair?
Michael Friendly's history of statistical graphics, The Golden Age of Statistical Graphics (Statistical Science, 2008), gives Playfair's dates as 1759 to 1823. It credits him with inventing the line graph and the bar chart in his 1786 *Commercial and Political Atlas*, followed by the pie chart and circle graph in his 1801 *Statistical Breviary*.
Ian Spence's paper on the pie chart, No Humble Pie (2005), adds that the pie chart's likely inspiration was the logic diagrams of Llull, Bruno, Leibniz and Euler, familiar to William through the teaching of his brother John, a mathematician.
What was the first bar chart?
Playfair's Atlas was mostly line graphs of England's imports, exports and debts across the eighteenth century, each plotted against years. One chart was different. The list of plates in the 1786 edition includes a chart of the exports and imports of Scotland for a single year, 1780 to 1781. With only one year there was no time axis to draw, so Playfair drew bars.
Friendly states the principle: Playfair invented comparative bar charts "to show relations of discrete series for which no time metric was available". That is still the rule. Use a line graph when the horizontal axis is time; use bars when you compare separate categories.
Why did Playfair think charts beat tables?
In the introduction to the 1801 edition of the Atlas (scan at the Internet Archive), Playfair wrote, in modernised spelling: "As the eye is the best judge of proportion, being able to estimate it with more quickness and accuracy than any other of our organs", charts suit any question about relative amounts. A table, he said, gives as many separate ideas to remember as there are sums, while a chart unites "proportion, progression, and quantity, all under one simple impression of vision".
He also answered critics who said that lengths on paper have nothing to do with money. Imagine a trader who stacks each day's guineas in a single pile, he wrote: each pile's height matches that day's takings. His "lineal arithmetic" was "nothing more than those piles of guineas represented on paper", where an inch might stand for five million guineas.
Worked example: drawing bars to scale
Use Playfair's own scale, 1 inch for 5 million guineas, with sample amounts.
Category A, 12.5 million: 12.5 ÷ 5 = 2.5 inches.
Category B, 7.5 million: 7.5 ÷ 5 = 1.5 inches.
Category C, 20 million: 20 ÷ 5 = 4 inches.
Check the ratios: C is 20 ÷ 12.5 = 1.6 times A, and its bar is 4 ÷ 2.5 = 1.6 times as long. The picture tells the truth.
Now break the rule. Suppose two sample results, 50 and 55, are drawn on an axis that starts at 45. The bars are 5 and 10 units long, so the second looks twice the first, although 55 is only 10% more than 50. Start the axis at zero and the bars are 50 and 55 units long, which looks like the small difference it is.
What mistakes do students make with bar charts?
Cutting the axis. As above, a bar chart's scale must start at zero, because the reader compares lengths.
Uneven widths or gaps. Bars should have equal widths and equal gaps, so that only length carries meaning.
Using bars for a time series. For data across many years a line graph shows the trend more clearly, as Playfair's own Atlas did.
Confusing bar charts with histograms. In a histogram the bars touch and the horizontal axis is a number line. Our post on Class 9 statistics covers the difference.
For a much older idea in graphing, see our post on Nicole Oresme, who drew speed against time in the 1300s.
If reading graphs in physics or chemistry still feels slow, the Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing, so you can revise the one idea that is blocking you.
What can a student learn from how Playfair worked?
Playfair started from a question about his readers, not his data: what can a busy person take in at a glance? He picked the form that matched the data, lines for time and bars for categories, and defended his choice with a plain example anyone could picture. When you draw a graph for a lab record, ask the same two questions: what should the reader see first, and does each length on the page match its number?
Try it now: write your last test marks in five subjects and draw them as a bar chart to scale, with the axis starting at zero.
