Populations, samples, and estimation

One of the core ideas of statistics is that we can use a subset of a group, study it, and then make inferences or conclusions about that much larger group.

For example, let's say we wanted to find the average (mean) weight of all the people in Germany. One way do to this is to visit all the 81 million people in Germany, record their weights, and then find the average. However, it is a far more sane endeavor to take down the weights of only a few hundred Germans, and use these to deduce the average weight of all Germans. In this case, the few hundred people we do measure is the sample, and the entirety of the people in Germany is called the population.

Now, there are Germans of all shapes and sizes: some heavier, some lighter. If we only pick a few Germans to weigh, we run the risk of, by chance, choosing a group of primarily underweight Germans or overweight ones. We might then come to an inaccurate conclusion about the weight of all Germans. However, as...