If it is reasonable to assume that a population consists of values that have a Gaussian distribution, then what will be the distribution of a property (a ‘statistic’) of a sample drawn from this Gaussian ‘parent’? The property might be the mean, variance or standard deviation of the sample. Each of these properties has a sampling distribution, which can be described as follows.

We imagine a very large or infinite population that has a Gaussian distribution with mean μand standard deviation ?. A sample consisting of n values is randomly drawn from this population. A property of the sample is calculated, in order to estimate the corresponding population parameter. We then draw another sample, also of size n, and calculate the same property for this second sample. The process is repeated many times. Next the distribution of that property is examined; the distribution becomes manifest as a result of taking a large number of repeated samples (all of size n). The distribution is the sampling distribution of the property in question. It is understood that, in any particular experimental situation, we do not actually need to draw a large number of samples; this process is a conceptual one that enables us to infer, from one actual sample, the variability (depicted by the shape of the sampling distribution) of our estimate of the population parameter. In section 9.1 we review the material already discussed in section 8.6.2.