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In the context of statistics, the word 'sample' refers to a subset of individuals or observations taken from a larger group known as a population. When describing a sample, it's critical to note its size, how it was selected, and the characteristics of the individuals within it.

Taking the example of the sociologist conducting surveys at a mall, the sample consists of 120 people interviewed about their cell phone use. If this sample were randomly selected from all mall visitors and represents various demographics—such as age, gender, and income levels—it could be considered representative of the mall's overall visitor population. Otherwise, the sample may be biased, which limits its usefulness for making inferences about the larger population. It's also essential to describe the method of selection. If the 120 individuals were chosen purely by chance, each person at the mall had an equal likelihood of being included, which is ideal for sample representativeness.

The term 'population' in field of statistics signifies the entire set of individuals or items of interest from which researchers may potentially collect data. The key characteristics of a population are that it includes all possible subjects that meet a set of predefined criteria and that the population is usually not fully surveyed due to its size.

For the sociologist in our mall survey example, the population can be described as all people who visit the mall. This broad group encompasses every possible visitor, and their collective cell phone usage patterns are what the sociologist aims to understand. When defining a population, it's vital to set clear boundaries to ensure the sample taken is appropriate for the research questions being explored—whether it is limited to a specific demographic, time frame, or other identifiable characteristic. By accurately defining the population, the sociologist can make authoritative statements about the whole group based on the collected data.

Generalizing survey results is the process of extending findings from a sample to the wider population it intends to represent. Achieving valid generalizations is the ultimate goal of many statistical studies. This process depends on the representativeness of the sample, the methodology of data collection, and the use of proper inferential statistical techniques.

For generalizations to be reliable, the sample must be an accurate microcosm of the population. If biases are introduced during sampling, such as selecting only those mall shoppers who appear tech-savvy, the generalizations from the sociologist's survey would be flawed. Adequate sampling techniques, including random sampling and stratified sampling among others, are used to reduce such biases. Furthermore, respondents should be surveyed under similar conditions to avoid introducing variability that is not present in the population.
The sociologist can then use statistical analysis to estimate the characteristics of the entire mall visitor population related to cell phone use, offering insights that can inform business decisions, marketing strategies, or further research inquiries.