The .Plan

In suburbia:

Mr. Mayer, who recently moved with his wife and three young children to New York, said he believed that it was important for children to grow up in a place that is racially, ethnically and economically diverse. He calls those places more vibrant. In most places, the upper middle class is less diverse than the middle, he said. New York would be less attractive to him without its still-expansive and lively middle.

“This trend toward living and interacting with people who are like you is intensifying a lot,” said Professor Gyourko, who lives in the affluent suburb of Swarthmore, Pa. “I do not meet the full range of incomes and social classes within my neighborhood. Well, think about what happens if metropolitan areas like New York, San Francisco and the like turn into my suburb. You’ll have even less interaction. The most interesting and potentially foreboding implication of this sorting is that it changes the way we view life.”
–Janny Scott, “Cities Shed Middle Class, and Are Richer and Poorer for It”, New York Times, July 23, 2006

The statisticians believed that the Germans, being Germans, had logically numbered their tanks in the order in which they were produced. And this deduction turned out to be right. It was enough to enable them to make an estimate of the total number of tanks that had been produced up to any given moment.

The basic idea was that the highest serial number among the captured tanks could be used to calculate the overall total. The German tanks were numbered as follows: 1, 2, 3 … N, where N was the desired total number of tanks produced. Imagine that they had captured five tanks, with serial numbers 20, 31, 43, 78 and 92. They now had a sample of five, with a maximum serial number of 92. Call the sample size S and the maximum serial number M. After some experimentation with other series, the statisticians reckoned that a good estimator of the number of tanks would probably be provided by the simple equation (M-1)(S+1)/S. In the example given, this translates to (92-1)(5+1)/5, which is equal to 109.2. Therefore the estimate of tanks produced at that time would be 109

By using this formula, statisticians reportedly estimated that the Germans produced 246 tanks per month between June 1940 and September 1942. At that time, standard intelligence estimates had believed the number was far, far higher, at around 1,400. After the war, the allies captured German production records, showing that the true number of tanks produced in those three years was 245 per month, almost exactly what the statisticians had calculated, and less than one fifth of what standard intelligence had thought likely.
–Gavyn Davies, “How a Statistical Formula Won the War”, The Guardian, July 20, 2006