Florence Nightingale

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Example 6: Student work

The Polar Area Diagrams of Florence Nightingale
If you read the article on Florence Nightingale in “The Children’s Book of Famous Lives”1 you will not learn that she had to battle with her parents to be allowed to study Mathematics. If you read the Ladybird book “Florence Nightingale”2 you will not discover that she was the first woman to be elected as a Fellow of the Royal Statistical Society. In looking around for an area of research I was intrigued to discover that Florence Nightingale, who I always thought of as the “lady with the lamp”, was a competent Mathematician who created her own type of statistical diagram which she used to save thousands of soldiers from needless death. Florence Nightingale headed a group of 38 nurses who went to clean up the hospitals for the British soldiers in the Crimea in 1854. She found that most of the deaths were due to diseases which could be prevented by basic hygiene, such as typhus and cholera. Her improvements were simple but they had an enormous effect: “She and her nurses washed and bathed the soldiers, laundered their linens, gave them clean beds to lie in, and fed them”3. When she returned to Britain she made a detailed report to the Government setting out what conditions were like and what needed to be done to reduce deaths in the hospitals. Nothing was done, so she tried again, making another statistical report and included in it three new statistical diagrams to make data collated by William Farr more accessible to people who could not get their minds around tables of figures. These were her polar area diagrams or rose diagrams, sometimes also known as ‘coxcombs’. The first showed how many men had died over the two years 1854-5, the second showed what proportions of men had died from wounds in battle, from disease and from other causes, the third showed how the number of deaths had decreased once “sanitary improvements”4 had been introduced. I decided I would try to recreate the second of these diagrams which is the most complicated and the most shocking. It is called “Diagram of the causes of mortality in the army in the east”. A copy of it is below:

Mathematics SL and HL teacher support material


Example 6: Student work

Figure 1

The basic ideas are very simple. The blue area represents deaths due to disease, the red area represents death due to wounds in battle and the black area represents death due to other causes. I tried to find a copy of the data which this diagram represented, but I had no luck, so I decided to make sure I understood exactly how the diagram was made and to make my own version of some data which I did have to hand. Once I tried to understand the diagram in detail I found there were some problems. The First Problem

I wasn’t sure whether the black area in a shape such as this: was supposed to be

this area

or this area

Mathematics SL and HL teacher support material


Example 6: Student work

In other words, were the colours separate, or overlapping? The articles I read didn’t make it clear. O’Connor says that “The area of each coloured wedge, measured from the centre as a common point, is in proportion to the statistic it represents”5, which makes it seem that all colours are wedged shaped, or sectors, so the colours overlap. However, Lienhard commented that in the November 1854 section “battle deaths take up a very small portion of each slice”6, which makes it sound as though the slice has three separate portions, and Brasseur says that “she also divided the areas within each of the wedges to show which portion of the mortality data for that month could be allotted to each cause of death”4. I decided to construct polar area diagrams for a set of data with the colours separate and with the colours overlapping to see if putting theory into practice would make it clearer to me. The data I used was taken from the IB grade distribution statistics for the past 15 years at my own institution. I...
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