Statistics means both data and analysis of that data. The history of mathematical analysis of statistics begins around 1890 with Karl Pearson. Much development of statistics took place between the World Wars but it was not until World War II that statistics became a tool of war. How many uniforms do you need? You have to make them before you have the personnel. When the inductee arrives he must be given his uniform and it must “fit”. Someone better have kept data on the population. If we make too many we are wasting resources that could go to some other activity. The British did not have such data at the start of the war.
One war story is the case of armor plate on aircraft. It is heavy and if it is not needed it will slow down the plane and use more fuel. A team recorded the locations of all the bullet holes in planes that had returned from battle. Then armor plate was placed at random in the places were no bullet holes were recorded. Why? Any bullet hole that was recorded was not a vital spot, the plane had returned. The planes hit in vital spots had never been seen.
The Nature of Statistics
by W. Allen Wallis and Harry V. Roberts is a paper back that one could have students read. The authors claim another title for their book could be “How to Live with Statistics, Without Actually Figuring”. Their second chapter is 26 short anecdotes of cases where statistics was used to solve a problem.
One of their cases is a study of the relationship between aircraft losses and the length of time since overhaul. It was found that the number of hours lost decreased as the time increased, the opposite of what was expected. So the length of time between overhauls was allowed to increase and the maintenance system improved so overhaul would increase the chances a plane would fly rather than decrease them. This points out that statistics is the scientific method. Being observant has unexpected rewards.
Another story Wallis and Roberts tell is how the Allies estimated German industrial output and capacity from the serial numbers on captured equipment. After the war it was found the Allies had the figures sooner than the Germans and were more accurate because the Germans waited for full counts.
One last war story. After the war the occupation forces required bakers to sell bread of a minimum weight. A professor kept track of his bread weights. He found they made a normal curve but the mean was lower than called for. He reported the baker to the authorities. They spoke to the baker and the professor’s loaves now were all over the required weight. He again reported the baker to the authorities and this time the baker was prosecuted. Why? The histogram was not normal. The baker was selling the professor only loaves from the heavy end and those who were not complaining were getting the rest.
Sampling is another source of stories. Rail Roads and Airlines have found it cheaper to sample inter-line billings than to calculate the exact amounts due by working out every bill. After all it takes time to do the bills.
There is popular literature on statistics and probability available for your students. It is just less frequent than Algebra, Geometry and Topology. Look for it. I am still looking for more.
Stories do not have to come from the literature. Look around you. One example I can think of is the geysers in Yellowstone National park. How do we know when to show up to see them? How do we know when it is not worth waiting any longer? Why is Old Faithful called Old Faithful? Records are kept and standard deviations are calculated.
The literature need not be math books. Frequently someone will write Ann Landers or some other columnist bewailing some behavior they observed. Is it probable? Could it just have happened by chance?