The previous chapter focused on measurements. Here we will talk more about how to extract quantitative information from a collection of measurements. The discussion will lead us into topics as diverse as flood and earthquake frequencies, election polls, and census taking. What can a poll of a small number of registered voters tell us about the likely outcome of a forthcoming election? What can we learn from the past history of flooding along a river that will give some indication of what we might expect in the future? Uncertainties are associated with each topic, uncertainties that arise from different sources and are quantified in different ways.

There are many processes and pathways that lead to ensembles of measurements. One very common source is simply making a number of measurements on a single object – each student in a class at the local elementary school measures the height of their teacher, or all seismograph stations in a region estimate the magnitude of yesterday's earthquake. A second common ensemble comprises one-time measurements of a number of different objects – perhaps the weight of each student in the class on the first morning of the new school term, or the concentration of arsenic in each water well in the county on a given day.