8.2 Sample
A finite set of objects drawn from the population with an aim is called a sample.
Even in every day life we make many of our decisions based on samples taken, though we are not aware of it. I met Jackson yesterday first time for an hour or two, I concluded that "Jackson is crazy" which may be wrong. We just take a little from a gunny bag of rice, we judge its quality and then we purchase the whole bag. If we want to taste milk, we just take a glassful of milk from the can and taste it. Note that taking a sample is easy in many cases where the population is uniform or homogeneous. When the population is heterogeneous (not uniform), the selection of a sample is not very easy.
The fundamental assumption underlying most of the theory of
sampling is random sampling. This consists of the selection
of individuals from the population in such a way that each individual
of the population has an equal chance of being selected i.e. a sample
so selected must be a true representative of the population.
The process of such selection is called random sampling.
The aim of the theory of sampling is to get as much information as possible, ideally all the information about the population from which the sample has been drawn. From the parent population, in particular, we would like to estimate the parameters of the population or specify the limits or ranges within which the population parameters are expected to lie with a specified degree of confidence.
The logic of the sampling theory is the logic of induction, that is, we go from particular (i.e sample) to general (i.e. population). Naturally all results will have to be expressed in terms of probability. In the theory of sampling, we often come across two words, 'parameters' and 'statistics'.
