Samples

A sample is a subset of the population, a set of n states of a random variable. Normally, statistical data are samples, however, most statistical techniques have been developed for populations. This gives rise to several aspects which have to be considered when working with statistical data:
 

(1) the equations derived for populations do not hold for samples if the sample space is small. In many cases there are special formulas for samples, which should be applied whenever you need to calculate a statistical descriptor for the sample. For example, the formula to calculate the variance is different for samples and for populations:
 
 

for populations	for samples

(2) The sample may not be representative for the population. A representative sample shows the same properties as the population.

(3) The distribution of sampled data may deviate from the distribution of the original data. This is especially true for samples which are obtained by automatic measurement devices with unknown preprocessing of the data (e.g. averaging).