Data Science & Theory Of Inference: Concept Of statistical population and sample from a population

 The concept of statistical population and sample from a population is fundamental in statistical analysis. A population is defined as the complete set of individuals or objects that possess certain characteristics that are of interest to the researcher. For example, if a researcher is interested in studying the purchasing habits of all consumers in the United States, the population, in this case, would be all consumers in the United States.

A sample, on the other hand, is a subset of the population that is selected for the purpose of the study. The sample is used to make inferences about the population from which it was drawn. For example, a researcher may choose to survey 1000 consumers in the United States to make inferences about the purchasing habits of all consumers in the United States.

It's important to note that the sample should be representative of the population so that the results from the sample can be generalized to the population. This means that the sample should be selected in such a way that it accurately reflects the characteristics of the population. The sample size should be large enough to ensure that the results are accurate and reliable.

In summary, a population refers to the entire group of individuals or objects that a researcher is interested in studying, while a sample is a subset of the population that is selected for the purpose of the study. The sample is used to make inferences about the population from which it was drawn, it should be representative of the population and the sample size should be large enough to ensure that the results are accurate and reliable.

There are several key differences between statistical populations and samples:

Definition: 

A population is the complete set of individuals or objects that possess certain characteristics that are of interest to a researcher, while a sample is a subset of the population that is selected for the purpose of study.

Size: 

Populations are typically large, often numbering in the thousands or millions, while samples are smaller, typically numbering in the dozens or hundreds.

Representativeness: 

Populations are generally more representative of the true characteristics of the individuals or objects being studied than samples, which may not be representative of the population.

Accessibility: 

Populations are often difficult to access, while samples are usually more accessible.

Purpose: 

The purpose of studying a population is to make inferences about the population, while the purpose of studying a sample is to make inferences about the population from which the sample was drawn.

Generalization: 

Populations are generalizations of the characteristics of the individuals or objects being studied, while samples are used to infer about the population.

Sample Error: 

Populations do not have sampling errors, while samples do. Sampling error is the difference between the sample statistics and population parameters.

Cost: 

Populations are generally more expensive to study than samples due to their large size.

In summary, statistical populations and samples have different characteristics, sizes, representativeness, accessibility, purpose, generalization, sample error, and cost.