Population, Sample, Census and Sample Survey

In business and economic analysis we rarely have direct access to every unit of a population — the complete set of items, people, or transactions under study (e.g., every customer of a bank, every unit produced in a year). A sample is a smaller, carefully chosen subset of the population that is actually observed, and the results found in the sample are used to draw conclusions (make inferences) about the population as a whole. This chapter is about how such samples are drawn and how far their results can be trusted — the same statistical principles are taught across Indian commerce and statistics curricula, and this syllabus follows that common treatment.

There are two broad approaches to collecting data on a population:

• Census (complete enumeration): every single unit of the population is examined. Example: a full statutory audit of a company's accounts, or the decennial Census of India that counts every citizen.
• Sample survey: only a part of the population is examined, and the findings are generalised to the whole. Example: a quality-control inspector checking 50 packets out of a day's production run of 10,000 packets, or a market-research agency surveying 500 consumers to judge the popularity of a new product across a city of lakhs of consumers.

A census gives the most complete and accurate picture in principle, but it is usually expensive, time-consuming and sometimes physically impossible (a light-bulb factory cannot test every bulb for its life in burning hours, because testing a bulb to failure destroys it). A well-designed sample survey is quicker, cheaper, and — perhaps surprisingly — often more reliable in practice, because the resources saved can be spent on better training of investigators and closer supervision of the smaller volume of work, cutting down the errors that creep into a rushed, poorly-supervised full census.

The branch of statistics that studies how to draw a sample and how to use it to estimate population characteristics (and to test claims about them) is called statistical inference — its two main tools, estimation and hypothesis testing, are both built on the idea of sampling and are covered later in this chapter.