Population and Samples

A population refers to the entire group of individuals or items that we are interested in studying, while a sample is a subset of the population that is selected for analysis.

Population

A population includes all members of a defined group. This group can be large or small, depending on the context. For example:

• All students in a university.
• Every household in a city.
• All manufactured products from a factory.

The population is denoted by the symbol \(N\).

Census

A census is a comprehensive data collection method that involves surveying every member of the population. It aims to obtain complete and accurate information about the population.

Example: The national census conducted every ten years aims to gather demographic data from every resident in a country.

Advantages of a census:

1. Provides complete data for the entire population.
2. Reduces sampling error since no sampling is involved.

Disadvantages of a census:

1. Time-consuming and costly.
2. Difficult to manage, especially with large populations.

Sample

A sample is a smaller group drawn from the population. It is used to make inferences or estimates about the population without needing to collect data from every individual. The sample size is denoted by the symbol nnn.

Example: If we want to study the average height of students in a university (population), we might select 100 students (sample) to represent the larger group.

Using a sample allows researchers to:

1. Save time and resources.
2. Obtain insights about a population without surveying every member.
3. Reduce logistical challenges associated with large populations.

Sampling Frame

A sampling frame is a list or database from which a sample is drawn. It includes all the members of the population that can be sampled and serves as a reference for selecting a sample.

Example: A list of all registered voters in a district can serve as a sampling frame for a study on voting behaviour.

Sampling Units

Sampling units are the individual members or items that make up the sample. Each unit is a part of the population from which data will be collected.

Example: In a study of student performance, each student selected from the population of students is considered a sampling unit.