Some key terminologies associated with statistics, specifically related to populations and samples:

1. Population: In statistics, the term "population" refers to the entire group or set of individuals, objects, or events that is of interest to a researcher or analyst. It represents the larger collection from which a sample is drawn and about which inferences are made. The population is the complete set of units or elements that possess the characteristics being studied. It can vary depending on the context and the research question at hand. For example, the population of interest could be:

- Human Population: If the study aims to investigate a specific characteristic of all humans, then the population would consist of every individual on Earth.

- Animal Population: If researchers are studying a particular species of animals, the population would encompass all individuals of that species in a specific area or habitat.

- Product Population: In market research, the population could be all the products or services available in a particular market or industry.

- Process Population: When studying a manufacturing process or system, the population would comprise all units or items produced by that process.

- Geographical Population: In studies related to geography or urban planning, the population might refer to all residents or households in a particular city, region, or country.

2. Sample: A sample is a subset or a smaller representative group selected from the larger population. It is used to gather information and make inferences about the population as a whole. Collecting data from an entire population can often be impractical or time-consuming, so samples are used to estimate population characteristics. In the example mentioned earlier, a sample might consist of a smaller group of adults randomly selected from the population.

In statistics, a sample refers to a subset or a smaller representative group that is selected from a larger population. It is a subset of the population from which data is collected and analyzed to draw inferences about the entire population. Sampling allows researchers to gather information efficiently and make statistical conclusions without studying the entire population, which can often be impractical or time-consuming.

Here are some key points about samples in statistics:

- Purpose: Samples are used to estimate population parameters or characteristics. By studying a smaller group (the sample), researchers can make inferences about the larger population from which the sample was drawn.

- Representativeness: It is crucial that a sample is representative of the population from which it is drawn. A representative sample accurately reflects the characteristics and diversity of the population, ensuring that the findings from the sample can be generalized to the population. Various sampling techniques are used to ensure representativeness, such as random sampling or stratified sampling.

- Sample Size: The size of a sample refers to the number of individuals or items included in the sample. The appropriate sample size depends on factors such as the desired level of precision, the variability in the population, and the research objectives. Larger sample sizes generally provide more reliable and precise estimates.

- Sampling Methods: Different sampling methods are employed based on the nature of the population and the research goals. Common sampling methods include simple random sampling (each member of the population has an equal chance of being selected), stratified sampling (population divided into subgroups, and samples are taken from each subgroup), cluster sampling (population divided into clusters, and some clusters are randomly selected), and systematic sampling (every nth member of the population is selected after an initial random starting point).

- Sampling Bias: Sampling bias occurs when the sample selected is not representative of the population, leading to biased or inaccurate results. Bias can arise from flaws in the sampling method, non-response bias (certain individuals refuse to participate), or selection bias (certain individuals are more likely to be included or excluded from the sample). Efforts should be made to minimize sampling bias and ensure the sample accurately reflects the population.

- Inference: Statistical inference involves drawing conclusions about the population based on the information obtained from the sample. Properly conducted sampling and statistical analyses allow researchers to make valid inferences about population parameters, such as means, proportions, or relationships.

3. Sampling: Sampling is the process of selecting individuals or items from a population to form a sample. Various sampling techniques are used, such as simple random sampling, stratified sampling, cluster sampling, or systematic sampling. The choice of sampling method depends on factors such as the population size, accessibility, and research objectives.

4. Parameter: In statistics, a parameter refers to a numerical summary or characteristic that describes a population. It is a fixed, but often unknown, value that we want to estimate or make inferences about based on sample data. Parameters provide important information about the population and are fundamental to statistical analysis and inference.

5. Statistic: A statistic is a numerical summary or characteristic calculated from a sample. It is used to estimate or infer information about the corresponding population parameter. For instance, the sample mean or sample proportion are statistics.

6. Representative Sample: A representative sample is a sample that accurately reflects the characteristics and diversity of the population. It is crucial to ensure that the sample represents the population well, allowing for valid generalizations and inferences.

7. Sampling Frame: A sampling frame is a list or a representation of the individuals or items in a population from which a sample is drawn. It serves as a basis for selecting the sample and should ideally include all members of the population.