In statistical terms, what approach is known as the study of a population by studying representative samples?

The approach referred to as the study of a population by examining representative samples is known as analysis. In statistics, analysis involves the examination of data to identify patterns, trends, or relationships within a larger population. By using representative samples, analysts can gather insights without needing to examine every individual within the population, which is often impractical due to resource constraints.

This method allows for inferential statistics, where conclusions about the entire population are drawn based on the analysis of sample data. It is an essential concept in research and data-driven decision-making, helping to generalize findings and improve understanding of the population as a whole.

In contrast, the other options do not specifically relate to this methodology. Synthesis involves combining different ideas or data to form a new whole, decomposition refers to breaking down complex problems into simpler parts, and observation generally refers to the act of watching or monitoring phenomena, which does not inherently require statistical methods or representative sampling. Thus, analysis is the process that precisely encapsulates the study of population dynamics through representative samples.