Harold Eddleston, a seventy-seven-year-old from Greater Manchester, was still reeling from a cancer diagnosis he had been given that week when, on a Saturday morning in February, 1998, he received the worst possible news. He would have to face the future alone: his beloved wife had died unexpectedly, from a heart attack.

Eddleston’s daughter, concerned for his health, called their family doctor, a well-respected local man named Harold Shipman. He came to the house, sat with her father, held his hand, and spoke to him tenderly. Pushed for a prognosis as he left, Shipman replied portentously, “I wouldn’t buy him any Easter eggs.” By Wednesday, Eddleston was dead; Dr. Shipman had murdered him.

Harold Shipman was one of the most prolific serial killers in history. In a twenty-three-year career as a mild-mannered and well-liked family doctor, he injected at least two hundred and fifteen of his patients with lethal doses of opiates. He was finally arrested in September, 1998, six months after Eddleston’s death.

David Spiegelhalter, the author of an important and comprehensive new book, “The Art of Statistics” (Basic), was one of the statisticians tasked by the ensuing public inquiry to establish whether the mortality rate of Shipman’s patients should have aroused suspicion earlier. Then a biostatistician at Cambridge, Spiegelhalter found that Shipman’s excess mortality—the number of his older patients who had died in the course of his career over the number that would be expected of an average doctor’s—was a hundred and seventy-four women and forty-nine men at the time of his arrest. The total closely matched the number of victims confirmed by the inquiry.

One person’s actions, written only in numbers, tell a profound story. They gesture toward the unimaginable grief caused by one man. But at what point do many deaths become too many deaths? How do you distinguish a suspicious anomaly from a run of bad luck? For that matter, how can we know in advance the number of people we expect to die? Each death is preceded by individual circumstances, private stories, and myriad reasons; what does it mean to wrap up all that uncertainty into a single number?

In 1825, the French Ministry of Justice ordered the creation of a national collection of crime records. It seems to have been the first of its kind anywhere in the world—the statistics of every arrest and conviction in the country, broken down by region, assembled and ready for analysis. It’s the kind of data set we take for granted now, but at the time it was extraordinarily novel. This was an early instance of Big Data—the first time that mathematical analysis had been applied in earnest to the messy and unpredictable realm of human behavior.

Or maybe not so unpredictable. In the early eighteen-thirties, a Belgian astronomer and mathematician named Adolphe Quetelet analyzed the numbers and discovered a remarkable pattern. The crime records were startlingly consistent. Year after year, irrespective of the actions of courts and prisons, the number of murders, rapes, and robberies reached almost exactly the same total. There is a “terrifying exactitude with which crimes reproduce themselves,” Quetelet said. “We know in advance how many individuals will dirty their hands with the blood of others. How many will be forgers, how many poisoners.”

To Quetelet, the evidence suggested that there was something deeper to discover. He developed the idea of a “Social Physics,” and began to explore the possibility that human lives, like planets, had an underlying mechanistic trajectory. There’s something unsettling in the idea that, amid the vagaries of choice, chance, and circumstance, mathematics can tell us something about what it is to be human. Yet Quetelet’s overarching findings still stand: at some level, human life can be quantified and predicted. We can now forecast, with remarkable accuracy, the number of women in Germany who will choose to have a baby each year, the number of car accidents in Canada, the number of plane crashes across the Southern Hemisphere, even the number of people who will visit a New York City emergency room on a Friday evening.

In some ways, this is what you would expect from any large, disordered system. Think about the predictable and quantifiable way that gases behave. It might be impossible to trace the movement of each individual gas molecule, but the uncertainty and disorder at the molecular level wash out when you look at the bigger picture. Similarly, larger regularities emerge from our individually unpredictable lives. It’s almost as though we woke up each morning with a chance, that day, of becoming a murderer, causing a car accident, deciding to propose to our partner, being fired from our job. “An assumption of ‘chance’ encapsulates all the inevitable unpredictability in the world,” Spiegelhalter writes.

But it’s one thing when your aim is to speak in general terms about who we are together, as a collective entity. The trouble comes when you try to go the other way—to learn something about us as individuals from how we behave as a collective. And, of course, those answers are often the ones we most want.

The dangers of making individual predictions from our collective characteristics were aptly demonstrated in a deal struck by the French lawyer André-François Raffray in 1965. He agreed to pay a ninety-year-old woman twenty-five hundred francs every month until her death, whereupon he would take possession of her apartment in Arles.

At the time, the average life expectancy of French women was 74.5 years, and Raffray, then forty-seven, no doubt thought he’d negotiated himself an auspicious contract. Unluckily for him, as Bill Bryson recounts in his new book, “The Body,” the woman was Jeanne Calment, who went on to become the oldest person on record. She survived for thirty-two years after their deal was signed, outliving Raffray, who died at seventy-seven. By then, he had paid more than twice the market value for an apartment he would never live in.

Raffray learned the hard way that people are not well represented by the average. As the mathematician Ian Stewart points out in “Do Dice Play God?” (Basic), the average person has one breast and one testicle. In large groups, the natural variability among human beings cancels out, the random zig being countered by the random zag; but that variability means that we can’t speak with certainty about the individual—a fact with wide-ranging consequences.

Every day, millions of people, David Spiegelhalter included, swallow a small white statin pill to reduce the risk of heart attack and stroke. If you are one of those people, and go on to live a long and happy life without ever suffering a heart attack, you have no way of knowing whether your daily statin was responsible or whether you were never going to have a heart attack in the first place. Of a thousand people who take statins for five years, the drugs will help only eighteen to avoid a major heart attack or stroke. And if you do find yourself having a heart attack you’ll never know whether it was delayed by taking the statin. “All I can ever know,” Spiegelhalter writes, “is that on average it benefits a large group of people like me.”

That’s the rule with preventive drugs: for most individuals, most of those drugs won’t do anything. The fact that they produce a collective benefit makes them worth taking. But it’s a pharmaceutical form of Pascal’s wager: you may as well act as though God were real (and believe that the drugs will work for you), because the consequences otherwise outweigh the inconvenience.