Nobody gets tosee everything.

Every week London printed its Bills of Mortality: christenings, burials and what each death was blamed on. John Graunt, a haberdasher, kept years of them and added them up. About 14 boys were christened for every 13 girls, year after year. Roughly a third of children died before six. London held about 384,000 people, not the two million some claimed.

Picture an urn with 3,000 white tokens and 2,000 black. Draw, note the color, replace, repeat. Jacob Bernoulli proved the share of white closes in on the true 60%, and worked out how fast: after 25,550 draws, landing between 58% and 62% is over a thousand times likelier than not. His book came out in 1713, after his death.

Abraham de Moivre, a Protestant who fled France, tutored mathematics in London, often in coffee houses. The chance of 4,900 to 5,100 heads in 10,000 tosses meant adding thousands of exact terms by hand. In November 1733 he found a shortcut: for many tosses, the counts trace a smooth bell, and the area under it gives the answer.

Thomas Bayes, a minister, died in 1761 with an essay among his papers. His friend Richard Price sent it to the Royal Society, where it was read in December 1763. It asked a question backwards: after some successes and failures, how sure can you be about the odds behind them? Spam filters still work this way.

In January 1801 Giuseppe Piazzi spotted Ceres and tracked it for about 40 days before it slipped into the Sun’s glare. Carl Friedrich Gauss, 24, worked out an orbit from those few, slightly wrong sightings. That December, Ceres turned up almost exactly where he said. His tool, he later wrote, was least squares: keep the squared misses smallest.

Florence Nightingale returned from the Crimean War sure soldiers were dying of the wrong things. With William Farr, she drew twelve wedges, one per month, sized by deaths and colored by cause. Blue, for preventable disease, swamped red, for wounds. It went into a confidential report in 1858. When army doctors pushed back, she passed copies to writers and reformers.

For an 1874 talk, Francis Galton built a board of pins. Beads bounced left or right at each pin. No one could say where a bead would land, but together they piled into the same bell every time. Galton also used statistics to argue for eugenics, a legacy the field still reckons with. Our front page runs the same machine.

William Sealy Gosset joined Guinness in 1899 as a chemist. His experiments ran on a handful of batches, but the formulas of the day assumed big samples and made small ones look surer than they were. His fix was a curve with fatter tails. Guinness didn’t let staff publish under their own names, so his 1908 paper was signed ‘Student’.

At tea at Rothamsted, Muriel Bristol said she could taste whether the milk went in first. Ronald Fisher later used it to show how to test any claim: pour eight cups, four each way, in random order, and ask her to pick the four milk-first. Guessing gets all four 1 time in 70. By most accounts, she got them all.

In 1936 the Literary Digest mailed about 10 million mock ballots, got about 2.4 million back, and called it for Alf Landon. Franklin Roosevelt carried 46 of 48 states. The lists leaned toward phone and car owners, and later studies found Landon voters were likelier to answer. George Gallup asked about 50,000 people chosen to mirror voters, and was right.

During the Second World War, Abraham Wald of Columbia’s Statistical Research Group studied where bombers were most vulnerable. The only data came from planes that returned, peppered with holes. The tempting move is to armor where the holes are. Wald saw that the sample was the clue: planes hit in the deadliest places mostly never came back to be counted.

In 1950 the Union of Japanese Scientists and Engineers (JUSE) invited the American statistician W. Edwards Deming, who taught hundreds of engineers and managers. His lesson, built on Walter Shewhart’s control charts: every process varies, so tell everyday wobble from a real signal, then shrink it. He gave back his royalties, and JUSE used them to found the Deming Prize.

The 2002 Oakland A’s spent about $42 million; the Yankees, about $133 million. Both won 103 games. Billy Beane and Paul DePodesta trusted the numbers over the scouts’ eye: getting on base drove runs far more than the market paid for. They bought walks cheaply. The A’s won 20 straight, then a league record, yet lost in the first round.

In March 2009 Douglas Bowman, Google’s first visual designer, quit and explained why on his blog. A team couldn’t decide between two blues, he wrote, so they tested 41 shades between them. Bowman felt data had crowded out judgment. The method now runs most of the web: random halves of visitors see two versions, and the difference decides.