# Random Sample = All ?

Taken from http://www.qualtrics.com/blog/are-you-practicing-random-selection/

In some situations, one person might desire to know something about some other people, whether it be the amount of money they make, the number of books they have read, the percentage of them who buy a certain product, or whatever this person might fancy to know. If the population considered is small enough and can be divided into groups with names that do not call for more clarification, it might not be too much of a problem to go and find this information by asking each person, assuming he or she tells the truth, and make claims about these groups.

Nevertheless, when the population is rather large, large enough that it would be extremely difficult to gather such information from each person, or too heterogeneous for a clear-cut categorization, a practice called random sampling, alongside a rather relaxed definition of names for groups is used, where a more manageable number of people from the population are supposed to be selected in an aleatory  way as to still find answers to questions about the whole population; in such case, one would say that the sample is representative of the population. Nonetheless, however careful this selection could be as to qualify it as random, can one really generalize it to the whole population? What is the mathematical basis, if any, for the belief (and confidence) that such generalization is possible? Before we get to these questions, let us look a little closer at what random sampling is.

The kind of information one would want to know such as the examples mentioned above is called a variable. In the case of the number of books, for each person of the population considered, a number would be assigned. Let’s say there are forty people; then, one can make many safe claims about the percentage of them who have read a certain number of books. However, for a very large and disparate population that cannot be managed too easily, a much smaller group is selected (sample) from this population so that one can hopefully arrive at some answers. The term “random” is attached to sample to say each person in the population has an equal chance of being selected. It happens there are many ways of making this sampling among which are simple random sampling, stratified random sampling, and multistage random sampling (Click here for more information about these types of sampling).