Population and Sample

Every study in Statistics begins with a clear idea of who or what is being studied. The Gujarat Board (GSHSEB) Std 11 Commerce Statistics syllabus — part of Business Mathematics and Statistics — starts the study of sampling with two foundational ideas: the population and the sample.

Population (or Universe) is the complete, well-defined set of all individuals, items, or observations that a study is interested in. It can be finite (all shops registered in a taluka) or very large (all transactions made on a payment app in a year).

Sample is a smaller, representative part of the population, actually selected and studied to draw conclusions about the whole population. A sample is meaningful only when it genuinely represents the population it is drawn from.

Example (business context): A company wants to know the average monthly spending of its 20,000 registered customers. The 20,000 customers form the population; if the company studies 500 randomly chosen customers instead of all 20,000, those 500 customers form the sample.

A few related terms used throughout this chapter:

• Sampling unit — the individual element of the population that is actually selected (a customer, a shop, a household).
• Sampling frame — the actual list or record from which sampling units are drawn (a customer database, an electoral roll, a list of registered firms).
• Parameter — a numerical characteristic of the population (e.g., the true population mean, denoted $\mu$).
• Statistic — a numerical characteristic computed from the sample (e.g., the sample mean, denoted $\bar{x}$), used to estimate the corresponding parameter.

Students preparing GSHSEB Std 11 Statistics questions and answers should be comfortable identifying the population, the sample, and the sampling frame in any given business or economic situation before choosing a sampling method.