Research Questions and Samples

Hello mathematicians, puzzlers, and other curious people!

An interesting piece of statistical analysis was performed during World War II. The goal was to improve airplanes so fewer would be shot down. In order to do so, they collected data from planes that made it back to base, marking the location of each piece of damage indicating that the plane had been hit by an enemy shot. When they gathered all that data onto one picture of a plane to draw conclusions from it, it looked something like this:

They agreed that the parts of the planes that were shot often (the ones covered in red dots) should get reinforced, to make the planes harder to shoot down.

At the last minute, however, someone pointed out a problem: the sample they were working from was planes that had made it back to the base. That meant that the plane already could handle taking some damage to the areas in red. The most important areas to reinforce, upon further consideration, were the areas that didn\’t have any red dots, because if an enemy bullet had ever hit a plane there, that plane didn\’t make it back to the base and into the sample.

Whenever you\’re researching, make sure you know how your sample is connected to your question.

Calc You Later!