Until the end of the eighteenth century, numbers were published in tables. A table is exact, but it forces the reader to compare row by row, holding values in their head. The data chart replaces that reading with a glance: differences, trends and peaks appear before a single number is read. Four charts show how this invention changed what could be seen.

Playfair invents the line chart

England's exports and imports with Africa, 1700 to 1780, in William Playfair's Commercial and Political Atlas (1786). The area between the two lines shows the balance of trade.
England’s exports and imports with Africa, 1700 to 1780, in William Playfair’s Commercial and Political Atlas (1786). The area between the two lines shows the balance of trade.William Playfair · Wikimedia Commons · public domain

In 1786 the Scotsman William Playfair, an engineer and pamphleteer with an eventful life, published The Commercial and Political Atlas, with 44 charts on English trade. There, for the first time in a systematic way, appear the line chart with time on the horizontal axis and the bar chart. In 1801 he added the pie chart. Playfair justified the drawings by saying that the eye grasps the shape of a series of numbers far better than memory holds the numbers.

Snow and the Broad Street pump

John Snow's map (1854) of the Soho district of London. Each cholera death is a small black bar stacked at the door of the house; the stacks cluster around the Broad Street water pump.
John Snow’s map (1854) of the Soho district of London. Each cholera death is a small black bar stacked at the door of the house; the stacks cluster around the Broad Street water pump.John Snow · Wikimedia Commons · public domain

In August and September 1854, a cholera epidemic killed hundreds of people in Soho, London. The dominant theory said the disease came from “miasma”, bad air. The physician John Snow suspected the water. He marked each death on a map of the district, with a small bar at the door of the house, and the stacks of bars piled up around a public water pump, the one on Broad Street. Snow persuaded the authorities to remove the pump’s handle, on 8 September.

The epidemic was already declining when the pump was disabled, and the most famous map was drawn afterwards, for the report. But the force of the argument lay in the drawing: the reader sees the source before reading any statistic. It is one of the landmarks of the birth of epidemiology.

Nightingale’s rose

Florence Nightingale's diagram of the causes of mortality in the British army in the East (1858). Each slice is a month; the blue area, deaths from preventable diseases; the red, from wounds; the black, from other causes.
Florence Nightingale’s diagram of the causes of mortality in the British army in the East (1858). Each slice is a month; the blue area, deaths from preventable diseases; the red, from wounds; the black, from other causes.Florence Nightingale · Wikimedia Commons · public domain

In the Crimean War, the English nurse Florence Nightingale saw that soldiers died far more from disease in filthy hospitals than from wounds in combat. On her return, in 1858, she had to persuade generals and ministers who did not read tables. She drew a new diagram, shaped like a rose: each month is a slice, and the area of each colour is proportional to the number of dead. The huge blue patch of preventable diseases swallowed the small red slice of wounds.

The mathematical detail matters. For the area to be proportional to the number, the radius of each slice has to be proportional to the square root of the number. Had she made the radius proportional to the number, the bad months would have looked much worse than they were. Nightingale was the first woman elected to the Royal Statistical Society, in 1858.

Minard and Napoleon’s march

The Russian campaign of 1812, by Charles Minard (1869). The width of the band is the size of the army: beige on the way to Moscow, black on the way back. Below, the temperature during the retreat.
The Russian campaign of 1812, by Charles Minard (1869). The width of the band is the size of the army: beige on the way to Moscow, black on the way back. Below, the temperature during the retreat.Charles Minard · Wikimedia Commons · public domain

In 1869 the French engineer Charles Minard drew Napoleon’s disastrous campaign in Russia. Six variables fit on a single sheet: the width of the band (the size of the army, from 422,000 men at the start to 10,000 on the return), the position on the map in two dimensions, the direction (going or returning), the temperature and the dates. The statistician Edward Tufte called it perhaps the best statistical graphic ever drawn.

Exercise: the radius of the rose

In one month, 4 times as many soldiers died as in another. If the areas of the slices are proportional to the dead, how many times larger should the radius be?

The area of a slice of fixed angle is proportional to the square of the radius. For the area to be 4 times larger, the radius must be $\sqrt4=2$ times larger. With the radius 4 times larger, the area would be 16 times larger, and the reader would see a difference exaggerated fourfold.

Exercise: Minard's army

The army set out with about 422,000 men and returned with about 10,000. What fraction survived? If the band were 1 cm wide on the return, how wide would it be at the start?

$\frac{10\,000}{422\,000}\approx2.4\%$. Since the width is proportional to the number of men, the band at the start would be $42.2$ cm wide. Minard drew the width proportional to the number, not to the square root, because he compares lengths, not areas.

Chapter index · ← From Oresme to the graph: drawing a quality that varies · The scale of a chart: when the drawing lies →