Representativeness of Samples

The need for choosing the right sample for a research investigation cannot be overemphasized. We know that a sample will rarely be the exact replica of the population from which it is drawn. For instance, very few sample means (X) are likely to be exactly to the population means (). Nor is the standard deviation of the sample (S) going to be the same as the standard deviation of the population (). However, if we choose the sample in a scientific way, we can be reasonably sure that the sample statistic (e.g. X, S, or S²) is fairly close to the population parameter (i.e., , , or ²). To put it differently, it is possible to choose the sample in such a way that it is representative of the population. There is always the slight probability, however, that sample values might fall outside the population parameters.