In statistics, a sample refers to a subset of individuals or items from a larger population. This subset is selected to represent the whole population in order to make statistical inferences. Here are some key points about samples:
- Definition: A sample is a segment of the population selected to participate in a study or survey. The selection process aims to be representative of the entire population to ensure that the results can be generalized.
- Types of Samples:
- Simple Random Sample: Every member of the population has an equal chance of being selected.
- Stratified Sample: The population is divided into homogeneous subgroups (strata) before sampling.
- Cluster Sample: The population is divided into clusters, and a random sample of these clusters is chosen.
- Systematic Sample: Every nth item from the list of population members is selected.
- Importance: Sampling is used because it is often impractical or impossible to study the entire population due to constraints like time, cost, or accessibility. It allows researchers to make predictions about the population with a known level of accuracy.
- Sampling Error: This is the error that arises due to the fact that the sample does not perfectly represent the population. Techniques like increasing sample size or improving the sampling method can reduce this error.
- History:
- The concept of sampling has roots in ancient times, but modern statistical sampling techniques began to develop in the 19th century with the work of statisticians like Adolphe Quetelet and Karl Pearson.
- Significant advancements were made in the 20th century by Jerzy Neyman, who formalized sampling theory, introducing concepts like sample size determination and stratified sampling.
- Applications: Sampling is used in numerous fields:
- Public Opinion Polls
- Quality Control
- Medical and Health Studies
- Market Research
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