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Most students know Florence Nightingale as a nurse. Fewer know she was also a statistician whose tables and diagrams changed how the British army looked after its soldiers. This post covers what her numbers showed, what happened in the hospitals at Scutari, a worked example on rates and on the area trick behind her famous diagrams, and what students can learn from how she used data.
Why did Nightingale turn to statistics?
During the Crimean War, British soldiers died in huge numbers. After the war, a Royal Commission examined the army's sanitary state. As the data designer RJ Andrews notes in a description of the Royal Commission's diagram of the Army in the East, Nightingale worked with Secretary at War Sidney Herbert, medical statistician William Farr and others between 1857 and 1859 to build an argument for better sanitation, using prose, tables and statistical graphics. In 1858 she became the Royal Statistical Society's first female member.
What did the numbers show?
Her 1858 pamphlet, Mortality of the British Army, reprinted from the Royal Commission's report, compared the army with civilians in England.
For every Englishman of army age who died at home, nearly 23 died in the war in the East.
Mortality in hospital from wounds "did not exceed 3 per cent. of the force, while the deaths from all causes were nearly 23 per cent. of the force in the field."
For every man of the same ages who died at home of "zymotic" diseases (fevers, cholera, diarrhoea, dysentery), 93 died in the army.
In January 1855 the army's death rate rose above the peak of London's Great Plague in September 1665. The pamphlet blamed poor shelter, wet clothing, poor food, no fuel to cook with, and badly chosen camp sites. Its verdict: the army in the Crimea "almost perished from zymotic disease."
What happened at Scutari?
Sick soldiers were shipped from the Crimea to hospitals around Scutari, on the Bosphorus. The pamphlet records that from the landing in the Crimea to the end of January 1855, 976 of 13,093 sick men shipped to Scutari died on a passage of only 300 miles. In January 1855, 10 of every 100 were lost on the voyage. In February, two of every five treated in the Bosphorus hospitals died, and one in two at Koulali, the worst of them. The buildings had poor drainage and ventilation, and the pamphlet calls them "little better than pest-houses."
Worked example: rates and the area trap
Part 1: a rate per 1,000.
Deaths on passage ÷ men shipped = 976 ÷ 13,093 ≈ 0.0745.
Per 1,000: 0.0745 × 1,000 ≈ 75. The pamphlet gives "75 per 1000".
Part 2: why area matters in a polar diagram. Nightingale's famous polar diagrams divide a circle into twelve wedges, one per month. The size of each wedge shows the deaths that month.
A wedge with angle θ and radius r has area ½ r^2 θ. All wedges share the same θ, so area is proportional to r^2.
Suppose one month had twice the deaths of another. If you made the radius twice as long, the area would be 2^2 = 4 times as big, and the picture would exaggerate the difference.
To show double the deaths, the radius must grow by √2 ≈ 1.41.
This is not just theory. Andrews describes how two early "batwing" charts in the Royal Commission report encoded quantity by distance from the centre, and were later refined by Nightingale and Farr so that the filled area represented the data.
Common mistakes: reading a polar chart by its radius instead of its area, and comparing totals instead of rates when groups differ in size. Our post on reading physics graphs covers the same habit of checking what a picture actually encodes.
What changed by the second winter?
By the winter of 1855-56, the pamphlet says, the men were well clothed, fed and sheltered, their huts were drained and ventilated, and nuisances had been removed. For January to June 1856 the army's mortality fell within the circle showing what it would have been at the death rate of Manchester, one of England's unhealthiest towns. "The men were the same, the conditions only had been altered."
What can a student take from Nightingale's way of working?
Split a total by cause. The breakdown, not the headline number, showed what could be fixed.
Choose a fair comparison. She compared soldiers with civilians of the same ages.
Design the picture to be honest. Area, not radius, should carry the data.
Her work sits well beside John Snow's cholera investigation, which also compared rates between groups. When concepts like rate, proportion or area of a sector are shaky, the Fermi Concept Library has a lesson for every concept in mathematics, each placed in a map so you can see what it builds on.
Next step: draw two wedges of the same angle for 100 and 200 deaths, choose the radii using the √2 rule, and check by measuring that the areas are in the ratio 1:2.
