We now begin a study of statistics. As well as being familiar with the mathematics that underpins the theoretical side of science we must also know how to analyse experimental data; for carrying out experiments, making measurements and collecting data are just as important in science as mathematical modelling.

Analysing experimental data is often fraught with difficulties, because one very important property, possessed by virtually any set of data values, is that different measurements of a given quantity will almost certainly show variation. This variation usually exists for one of two reasons. Firstly, variation could be present in what is being measured. For example, heights of people vary, daily hours of sunshine vary, the number of radioactive particles entering a geiger counter in a given time interval varies, and so on. Or, secondly, when measuring some fixed quantity, variation could arise due to errors of one kind or another creeping into the measuring process. We might, for example, take a sample of blood and analyse the blood for alcohol content. Even though we might use the same analytical technique, repeated determinations of the fixed concentration of alcohol would vary due to experimental error.

This variability not only affects the sort of conclusions we can draw from experimental data, but inevitably it means that in the first place we have to make repeated measurements of a quantity before we can say anything sensible about its value.