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The phenomenon being analyzed should be represented in all forms in the sample. Minima and maxima are of particular importance. For the precipitation example this means that stations with peak values should be present in the sample. However, if we are planning our own sampling scheme we usually do not know whether or not we have recorded the locations of minima and maxima.
As mentioned earlier, the spatial dependence of data among themselves is a very important prerequisite for a meaningful analysis. This relationship should be homogenous over the entire study area! Take the example of the precipitation monitoring stations: two stations at a distance of 2 km, for example should both have similar values in Ticino as well as in Jura, Fribourg, or Grison etc. This prerequisite is also called "stationarity".
Spatial distribution is of great importance. It can be completely random, regular, or clustered. You can see examples of these distributions below in the "Typology" section. An indication about the spatial distribution of a sample can be statistically obtained by using the "nearest neighbor" method, for example. It is one of the "point pattern analysis" techniques, i.e. methods that can help statistically characterize and analyze the spatial distribution of points.
The size, i.e. the number of samples, depends on the phenomenon and the surface area. In some cases, practical limitations constrain the sample size. Think of measurements in difficult terrain, or technically complex and expensive measurements. It is impossible to provide an ideal sample size for any task.