The London Bills of Mortality: how did statistics become a science?

Q: What was "political arithmetic"?

Graunt's friend, the physician and economist William Petty, supported this approach and named it "political arithmetic". Petty later applied a similar method to data from Ireland. The two of them together are regarded as the founders of the English school of "political arithmetic". The idea was this: affairs of state should be discussed not in words but in terms of number, weight and measure. Some have speculated that the book was actually written by Petty, but the encyclopedias consider this view to lack sufficient grounds.

In 17th-century London "bills of mortality" (Bills of Mortality) were issued every week: how many people had been buried in each church parish and how many children had been christened. Most people leafed through them only to find out whether the plague was approaching. John Graunt, however, decided to collect them over the years and arrange them in tables.

What did Graunt find in the bills?

In 1662 his short book came out: "Natural and Political Observations Made upon the Bills of Mortality". The Encyclopedia of Mathematics calls it the first treatise on vital statistics.

What Graunt did: - He proposed a method of calculating London's population from the annual numbers of christenings and burials. At the time exaggerated claims about the size of the city were going around, and he checked them not by guesswork but by calculation - He gave the first precise data on the ratio of boys to girls - According to the Encyclopedia of Mathematics, he drew up the first life table: about how many people live to what age

Later the statistician Karl Pearson regarded Graunt as the father of modern statistics. Many also know him as one of the founders of demography.

How Graunt's method works (prepared by the author, hypothetical figures). In the "Yangi Bozor" neighbourhood 120 babies were registered in one year. From an exact count in another neighbourhood it is known that there are 30 births a year per 1 000 inhabitants.

Step	Calculation	Result
Number of births	From the register	120
Births per 1 000 people	From the sample neighbourhood	30
Population estimate	120 ÷ 30 × 1 000	about 4 000 people

Graunt's calculating tools were paper, ink and hand-drawn tables: he copied the numbers by year by hand, added them up and calculated the ratios.

Estimating an entire population through a known indicator and a ratio, without going from house to house: this is one of the most important ideas of statistics. It also has a weak spot: if the sample neighbourhood is not like the others, the error will be large.

What was "political arithmetic"?

Graunt's friend, the physician and economist William Petty, supported this approach and named it "political arithmetic". Petty later applied a similar method to data from Ireland. The two of them together are regarded as the founders of the English school of "political arithmetic".

The idea was this: affairs of state should be discussed not in words but in terms of number, weight and measure. Some have speculated that the book was actually written by Petty, but the encyclopedias consider this view to lack sufficient grounds.

Then and now

Aspect	1662, London	Today
Data source	The churches' weekly bills	State civil registry offices and electronic registers
Who calculates	A lone amateur researcher	National statistics committees
Population size	Estimated through a ratio	The census and current population accounts
Life table	A first rough attempt	The basis of insurance and pension calculations

Graunt did not stop at counting: he drew conclusions from the numbers. It was at exactly this point that statistics turned from a register into a science.